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\begin{array}{c}\phantom{\times9999}25213\\\underline{\times\phantom{9999}36784}\\\end{array}
First line up the numbers vertically and match the places from the right like this.
\begin{array}{c}\phantom{\times9999}25213\\\underline{\times\phantom{9999}36784}\\\phantom{\times999}100852\\\end{array}
Now multiply the first number with the 1^{st} digit in 2^{nd} number to get intermediate results. That is Multiply 25213 with 4. Write the result 100852 at the end leaving 0 spaces to the right like this.
\begin{array}{c}\phantom{\times9999}25213\\\underline{\times\phantom{9999}36784}\\\phantom{\times999}100852\\\phantom{\times99}201704\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 25213 with 8. Write the result 201704 at the end leaving 1 spaces to the right like this.
\begin{array}{c}\phantom{\times9999}25213\\\underline{\times\phantom{9999}36784}\\\phantom{\times999}100852\\\phantom{\times99}201704\phantom{9}\\\phantom{\times9}176491\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 25213 with 7. Write the result 176491 at the end leaving 2 spaces to the right like this.
\begin{array}{c}\phantom{\times9999}25213\\\underline{\times\phantom{9999}36784}\\\phantom{\times999}100852\\\phantom{\times99}201704\phantom{9}\\\phantom{\times9}176491\phantom{99}\\\phantom{\times}151278\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 25213 with 6. Write the result 151278 at the end leaving 3 spaces to the right like this.
\begin{array}{c}\phantom{\times9999}25213\\\underline{\times\phantom{9999}36784}\\\phantom{\times999}100852\\\phantom{\times99}201704\phantom{9}\\\phantom{\times9}176491\phantom{99}\\\phantom{\times}151278\phantom{999}\\\underline{\phantom{\times}75639\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 25213 with 3. Write the result 75639 at the end leaving 4 spaces to the right like this.
\begin{array}{c}\phantom{\times9999}25213\\\underline{\times\phantom{9999}36784}\\\phantom{\times999}100852\\\phantom{\times99}201704\phantom{9}\\\phantom{\times9}176491\phantom{99}\\\phantom{\times}151278\phantom{999}\\\underline{\phantom{\times}75639\phantom{9999}}\\\phantom{\times}927434992\end{array}
Now add the intermediate results to get final answer.