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\begin{array}{c}\phantom{\times}978266262\\\underline{\times\phantom{999999}962}\\\end{array}
First line up the numbers vertically and match the places from the right like this.
\begin{array}{c}\phantom{\times}978266262\\\underline{\times\phantom{999999}962}\\\phantom{\times}1956532524\\\end{array}
Now multiply the first number with the 1^{st} digit in 2^{nd} number to get intermediate results. That is Multiply 978266262 with 2. Write the result 1956532524 at the end leaving 0 spaces to the right like this.
\begin{array}{c}\phantom{\times}978266262\\\underline{\times\phantom{999999}962}\\\phantom{\times}1956532524\\\phantom{\times}1574630276\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 978266262 with 6. Write the result 1574630276 at the end leaving 1 spaces to the right like this.
\begin{array}{c}\phantom{\times}978266262\\\underline{\times\phantom{999999}962}\\\phantom{\times}1956532524\\\phantom{\times}1574630276\phantom{9}\\\underline{\phantom{\times}214461766\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 978266262 with 9. Write the result 214461766 at the end leaving 2 spaces to the right like this.
\begin{array}{c}\phantom{\times}978266262\\\underline{\times\phantom{999999}962}\\\phantom{\times}1956532524\\\phantom{\times}1574630276\phantom{9}\\\underline{\phantom{\times}214461766\phantom{99}}\\\phantom{\times}494306220\end{array}
Now add the intermediate results to get final answer.