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\begin{array}{c}\phantom{\times999}7410963\\\underline{\times\phantom{99999}48821}\\\end{array}
First line up the numbers vertically and match the places from the right like this.
\begin{array}{c}\phantom{\times999}7410963\\\underline{\times\phantom{99999}48821}\\\phantom{\times999}7410963\\\end{array}
Now multiply the first number with the 1^{st} digit in 2^{nd} number to get intermediate results. That is Multiply 7410963 with 1. Write the result 7410963 at the end leaving 0 spaces to the right like this.
\begin{array}{c}\phantom{\times999}7410963\\\underline{\times\phantom{99999}48821}\\\phantom{\times999}7410963\\\phantom{\times9}14821926\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 7410963 with 2. Write the result 14821926 at the end leaving 1 spaces to the right like this.
\begin{array}{c}\phantom{\times999}7410963\\\underline{\times\phantom{99999}48821}\\\phantom{\times999}7410963\\\phantom{\times9}14821926\phantom{9}\\\phantom{\times}59287704\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 7410963 with 8. Write the result 59287704 at the end leaving 2 spaces to the right like this.
\begin{array}{c}\phantom{\times999}7410963\\\underline{\times\phantom{99999}48821}\\\phantom{\times999}7410963\\\phantom{\times9}14821926\phantom{9}\\\phantom{\times}59287704\phantom{99}\\\phantom{\times}59287704\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 7410963 with 8. Write the result 59287704 at the end leaving 3 spaces to the right like this.
\begin{array}{c}\phantom{\times999}7410963\\\underline{\times\phantom{99999}48821}\\\phantom{\times999}7410963\\\phantom{\times9}14821926\phantom{9}\\\phantom{\times}59287704\phantom{99}\\\phantom{\times}59287704\phantom{999}\\\underline{\phantom{\times}29643852\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 7410963 with 4. Write the result 29643852 at the end leaving 4 spaces to the right like this.
\begin{array}{c}\phantom{\times999}7410963\\\underline{\times\phantom{99999}48821}\\\phantom{\times999}7410963\\\phantom{\times9}14821926\phantom{9}\\\phantom{\times}59287704\phantom{99}\\\phantom{\times}59287704\phantom{999}\\\underline{\phantom{\times}29643852\phantom{9999}}\\\phantom{\times}1033371759\end{array}
Now add the intermediate results to get final answer.