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\begin{array}{c}\phantom{\times}1234567890\\\underline{\times\phantom{}1234567890}\\\end{array}
First line up the numbers vertically and match the places from the right like this.
\begin{array}{c}\phantom{\times}1234567890\\\underline{\times\phantom{}1234567890}\\\phantom{\times999999999}0\\\end{array}
Now multiply the first number with the 1^{st} digit in 2^{nd} number to get intermediate results. That is Multiply 1234567890 with 0. Write the result 0 at the end leaving 0 spaces to the right like this.
\begin{array}{c}\phantom{\times}1234567890\\\underline{\times\phantom{}1234567890}\\\phantom{\times999999999}0\\\phantom{\times99999999}-1773790878\phantom{9}\\\end{array}
Now multiply the first number with the 2^{nd} digit in 2^{nd} number to get intermediate results. That is Multiply 1234567890 with 9. Write the result -1773790878 at the end leaving 1 spaces to the right like this.
\begin{array}{c}\phantom{\times}1234567890\\\underline{\times\phantom{}1234567890}\\\phantom{\times999999999}0\\\phantom{\times99999999}-1773790878\phantom{9}\\\phantom{\times}1286608528\phantom{99}\\\end{array}
Now multiply the first number with the 3^{rd} digit in 2^{nd} number to get intermediate results. That is Multiply 1234567890 with 8. Write the result 1286608528 at the end leaving 2 spaces to the right like this.
\begin{array}{c}\phantom{\times}1234567890\\\underline{\times\phantom{}1234567890}\\\phantom{\times999999999}0\\\phantom{\times99999999}-1773790878\phantom{9}\\\phantom{\times}1286608528\phantom{99}\\\phantom{\times}52040638\phantom{999}\\\end{array}
Now multiply the first number with the 4^{th} digit in 2^{nd} number to get intermediate results. That is Multiply 1234567890 with 7. Write the result 52040638 at the end leaving 3 spaces to the right like this.
\begin{array}{c}\phantom{\times}1234567890\\\underline{\times\phantom{}1234567890}\\\phantom{\times999999999}0\\\phantom{\times99999999}-1773790878\phantom{9}\\\phantom{\times}1286608528\phantom{99}\\\phantom{\times}52040638\phantom{999}\\\phantom{\times99999}-1182527252\phantom{9999}\\\end{array}
Now multiply the first number with the 5^{th} digit in 2^{nd} number to get intermediate results. That is Multiply 1234567890 with 6. Write the result -1182527252 at the end leaving 4 spaces to the right like this.
\begin{array}{c}\phantom{\times}1234567890\\\underline{\times\phantom{}1234567890}\\\phantom{\times999999999}0\\\phantom{\times99999999}-1773790878\phantom{9}\\\phantom{\times}1286608528\phantom{99}\\\phantom{\times}52040638\phantom{999}\\\phantom{\times99999}-1182527252\phantom{9999}\\\phantom{\times}1877872154\phantom{99999}\\\end{array}
Now multiply the first number with the 6^{th} digit in 2^{nd} number to get intermediate results. That is Multiply 1234567890 with 5. Write the result 1877872154 at the end leaving 5 spaces to the right like this.
\begin{array}{c}\phantom{\times}1234567890\\\underline{\times\phantom{}1234567890}\\\phantom{\times999999999}0\\\phantom{\times99999999}-1773790878\phantom{9}\\\phantom{\times}1286608528\phantom{99}\\\phantom{\times}52040638\phantom{999}\\\phantom{\times99999}-1182527252\phantom{9999}\\\phantom{\times}1877872154\phantom{99999}\\\phantom{\times}643304264\phantom{999999}\\\end{array}
Now multiply the first number with the 7^{th} digit in 2^{nd} number to get intermediate results. That is Multiply 1234567890 with 4. Write the result 643304264 at the end leaving 6 spaces to the right like this.
\begin{array}{c}\phantom{\times}1234567890\\\underline{\times\phantom{}1234567890}\\\phantom{\times999999999}0\\\phantom{\times99999999}-1773790878\phantom{9}\\\phantom{\times}1286608528\phantom{99}\\\phantom{\times}52040638\phantom{999}\\\phantom{\times99999}-1182527252\phantom{9999}\\\phantom{\times}1877872154\phantom{99999}\\\phantom{\times}643304264\phantom{999999}\\\phantom{\times99}-591263626\phantom{9999999}\\\end{array}
Now multiply the first number with the 8^{th} digit in 2^{nd} number to get intermediate results. That is Multiply 1234567890 with 3. Write the result -591263626 at the end leaving 7 spaces to the right like this.
\begin{array}{c}\phantom{\times}1234567890\\\underline{\times\phantom{}1234567890}\\\phantom{\times999999999}0\\\phantom{\times99999999}-1773790878\phantom{9}\\\phantom{\times}1286608528\phantom{99}\\\phantom{\times}52040638\phantom{999}\\\phantom{\times99999}-1182527252\phantom{9999}\\\phantom{\times}1877872154\phantom{99999}\\\phantom{\times}643304264\phantom{999999}\\\phantom{\times99}-591263626\phantom{9999999}\\\phantom{\times9}-1825831516\phantom{99999999}\\\end{array}
Now multiply the first number with the 9^{th} digit in 2^{nd} number to get intermediate results. That is Multiply 1234567890 with 2. Write the result -1825831516 at the end leaving 8 spaces to the right like this.
\begin{array}{c}\phantom{\times}1234567890\\\underline{\times\phantom{}1234567890}\\\phantom{\times999999999}0\\\phantom{\times99999999}-1773790878\phantom{9}\\\phantom{\times}1286608528\phantom{99}\\\phantom{\times}52040638\phantom{999}\\\phantom{\times99999}-1182527252\phantom{9999}\\\phantom{\times}1877872154\phantom{99999}\\\phantom{\times}643304264\phantom{999999}\\\phantom{\times99}-591263626\phantom{9999999}\\\phantom{\times9}-1825831516\phantom{99999999}\\\underline{\phantom{\times}1234567890\phantom{999999999}}\\\end{array}
Now multiply the first number with the 10^{th} digit in 2^{nd} number to get intermediate results. That is Multiply 1234567890 with 1. Write the result 1234567890 at the end leaving 9 spaces to the right like this.
\begin{array}{c}\phantom{\times}1234567890\\\underline{\times\phantom{}1234567890}\\\phantom{\times999999999}0\\\phantom{\times99999999}-1773790878\phantom{9}\\\phantom{\times}1286608528\phantom{99}\\\phantom{\times}52040638\phantom{999}\\\phantom{\times99999}-1182527252\phantom{9999}\\\phantom{\times}1877872154\phantom{99999}\\\phantom{\times}643304264\phantom{999999}\\\phantom{\times99}-591263626\phantom{9999999}\\\phantom{\times9}-1825831516\phantom{99999999}\\\underline{\phantom{\times}1234567890\phantom{999999999}}\\\phantom{\times}304084036\end{array}
Now add the intermediate results to get final answer.