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\begin{array}{c}\phantom{\times99}78642198\\\underline{\times\phantom{999999}9465}\\\end{array}
First line up the numbers vertically and match the places from the right like this.
\begin{array}{c}\phantom{\times99}78642198\\\underline{\times\phantom{999999}9465}\\\phantom{\times9}393210990\\\end{array}
Now multiply the first number with the 1^{st} digit in 2^{nd} number to get intermediate results. That is Multiply 78642198 with 5. Write the result 393210990 at the end leaving 0 spaces to the right like this.
\begin{array}{c}\phantom{\times99}78642198\\\underline{\times\phantom{999999}9465}\\\phantom{\times9}393210990\\\phantom{\times}471853188\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 78642198 with 6. Write the result 471853188 at the end leaving 1 spaces to the right like this.
\begin{array}{c}\phantom{\times99}78642198\\\underline{\times\phantom{999999}9465}\\\phantom{\times9}393210990\\\phantom{\times}471853188\phantom{9}\\\phantom{\times}314568792\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 78642198 with 4. Write the result 314568792 at the end leaving 2 spaces to the right like this.
\begin{array}{c}\phantom{\times99}78642198\\\underline{\times\phantom{999999}9465}\\\phantom{\times9}393210990\\\phantom{\times}471853188\phantom{9}\\\phantom{\times}314568792\phantom{99}\\\underline{\phantom{\times}707779782\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 78642198 with 9. Write the result 707779782 at the end leaving 3 spaces to the right like this.
\begin{array}{c}\phantom{\times99}78642198\\\underline{\times\phantom{999999}9465}\\\phantom{\times9}393210990\\\phantom{\times}471853188\phantom{9}\\\phantom{\times}314568792\phantom{99}\\\underline{\phantom{\times}707779782\phantom{999}}\\\phantom{\times}1319061862\end{array}
Now add the intermediate results to get final answer.