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\begin{array}{c}\phantom{\times}1000000678\\\underline{\times\phantom{}198700483}\\\end{array}
First line up the numbers vertically and match the places from the right like this.
\begin{array}{c}\phantom{\times}1000000678\\\underline{\times\phantom{}198700483}\\\phantom{\times}-1294965262\\\end{array}
Now multiply the first number with the 1^{st} digit in 2^{nd} number to get intermediate results. That is Multiply 1000000678 with 3. Write the result -1294965262 at the end leaving 0 spaces to the right like this.
\begin{array}{c}\phantom{\times}1000000678\\\underline{\times\phantom{}198700483}\\\phantom{\times}-1294965262\\\phantom{\times}-589929168\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 1000000678 with 8. Write the result -589929168 at the end leaving 1 spaces to the right like this.
\begin{array}{c}\phantom{\times}1000000678\\\underline{\times\phantom{}198700483}\\\phantom{\times}-1294965262\\\phantom{\times}-589929168\phantom{9}\\\phantom{\times}-294964584\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 1000000678 with 4. Write the result -294964584 at the end leaving 2 spaces to the right like this.
\begin{array}{c}\phantom{\times}1000000678\\\underline{\times\phantom{}198700483}\\\phantom{\times}-1294965262\\\phantom{\times}-589929168\phantom{9}\\\phantom{\times}-294964584\phantom{99}\\\phantom{\times}0\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 1000000678 with 0. Write the result 0 at the end leaving 3 spaces to the right like this.
\begin{array}{c}\phantom{\times}1000000678\\\underline{\times\phantom{}198700483}\\\phantom{\times}-1294965262\\\phantom{\times}-589929168\phantom{9}\\\phantom{\times}-294964584\phantom{99}\\\phantom{\times}0\phantom{999}\\\phantom{\times}0\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 1000000678 with 0. Write the result 0 at the end leaving 4 spaces to the right like this.
\begin{array}{c}\phantom{\times}1000000678\\\underline{\times\phantom{}198700483}\\\phantom{\times}-1294965262\\\phantom{\times}-589929168\phantom{9}\\\phantom{\times}-294964584\phantom{99}\\\phantom{\times}0\phantom{999}\\\phantom{\times}0\phantom{9999}\\\phantom{\times}-1589929846\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 1000000678 with 7. Write the result -1589929846 at the end leaving 5 spaces to the right like this.
\begin{array}{c}\phantom{\times}1000000678\\\underline{\times\phantom{}198700483}\\\phantom{\times}-1294965262\\\phantom{\times}-589929168\phantom{9}\\\phantom{\times}-294964584\phantom{99}\\\phantom{\times}0\phantom{999}\\\phantom{\times}0\phantom{9999}\\\phantom{\times}-1589929846\phantom{99999}\\\phantom{\times}-589929168\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 1000000678 with 8. Write the result -589929168 at the end leaving 6 spaces to the right like this.
\begin{array}{c}\phantom{\times}1000000678\\\underline{\times\phantom{}198700483}\\\phantom{\times}-1294965262\\\phantom{\times}-589929168\phantom{9}\\\phantom{\times}-294964584\phantom{99}\\\phantom{\times}0\phantom{999}\\\phantom{\times}0\phantom{9999}\\\phantom{\times}-1589929846\phantom{99999}\\\phantom{\times}-589929168\phantom{999999}\\\phantom{\times}410071510\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 1000000678 with 9. Write the result 410071510 at the end leaving 7 spaces to the right like this.
\begin{array}{c}\phantom{\times}1000000678\\\underline{\times\phantom{}198700483}\\\phantom{\times}-1294965262\\\phantom{\times}-589929168\phantom{9}\\\phantom{\times}-294964584\phantom{99}\\\phantom{\times}0\phantom{999}\\\phantom{\times}0\phantom{9999}\\\phantom{\times}-1589929846\phantom{99999}\\\phantom{\times}-589929168\phantom{999999}\\\phantom{\times}410071510\phantom{9999999}\\\underline{\phantom{\times}1000000678\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 1000000678 with 1. Write the result 1000000678 at the end leaving 8 spaces to the right like this.
\begin{array}{c}\phantom{\times}1000000678\\\underline{\times\phantom{}198700483}\\\phantom{\times}-1294965262\\\phantom{\times}-589929168\phantom{9}\\\phantom{\times}-294964584\phantom{99}\\\phantom{\times}0\phantom{999}\\\phantom{\times}0\phantom{9999}\\\phantom{\times}-1589929846\phantom{99999}\\\phantom{\times}-589929168\phantom{999999}\\\phantom{\times}410071510\phantom{9999999}\\\underline{\phantom{\times}1000000678\phantom{99999999}}\\\phantom{\times}-1211527054\end{array}
Now add the intermediate results to get final answer.