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\begin{array}{c}\phantom{\times}10090199\\\underline{\times\phantom{}903201}\\\end{array}
First line up the numbers vertically and match the places from the right like this.
\begin{array}{c}\phantom{\times}10090199\\\underline{\times\phantom{}903201}\\\phantom{\times}10090199\\\end{array}
Now multiply the first number with the 1^{st} digit in 2^{nd} number to get intermediate results. That is Multiply 10090199 with 1. Write the result 10090199 at the end leaving 0 spaces to the right like this.
\begin{array}{c}\phantom{\times}10090199\\\underline{\times\phantom{}903201}\\\phantom{\times}10090199\\\phantom{\times}0\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 10090199 with 0. Write the result 0 at the end leaving 1 spaces to the right like this.
\begin{array}{c}\phantom{\times}10090199\\\underline{\times\phantom{}903201}\\\phantom{\times}10090199\\\phantom{\times}0\phantom{9}\\\phantom{\times}20180398\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 10090199 with 2. Write the result 20180398 at the end leaving 2 spaces to the right like this.
\begin{array}{c}\phantom{\times}10090199\\\underline{\times\phantom{}903201}\\\phantom{\times}10090199\\\phantom{\times}0\phantom{9}\\\phantom{\times}20180398\phantom{99}\\\phantom{\times}30270597\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 10090199 with 3. Write the result 30270597 at the end leaving 3 spaces to the right like this.
\begin{array}{c}\phantom{\times}10090199\\\underline{\times\phantom{}903201}\\\phantom{\times}10090199\\\phantom{\times}0\phantom{9}\\\phantom{\times}20180398\phantom{99}\\\phantom{\times}30270597\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 10090199 with 0. Write the result 0 at the end leaving 4 spaces to the right like this.
\begin{array}{c}\phantom{\times}10090199\\\underline{\times\phantom{}903201}\\\phantom{\times}10090199\\\phantom{\times}0\phantom{9}\\\phantom{\times}20180398\phantom{99}\\\phantom{\times}30270597\phantom{999}\\\phantom{\times}0\phantom{9999}\\\underline{\phantom{\times}90811791\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 10090199 with 9. Write the result 90811791 at the end leaving 5 spaces to the right like this.
\begin{array}{c}\phantom{\times}10090199\\\underline{\times\phantom{}903201}\\\phantom{\times}10090199\\\phantom{\times}0\phantom{9}\\\phantom{\times}20180398\phantom{99}\\\phantom{\times}30270597\phantom{999}\\\phantom{\times}0\phantom{9999}\\\underline{\phantom{\times}90811791\phantom{99999}}\\\phantom{\times}-442775113\end{array}
Now add the intermediate results to get final answer.