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\begin{array}{c}\phantom{\times999}167527\\\underline{\times\phantom{9999}78663}\\\end{array}
First line up the numbers vertically and match the places from the right like this.
\begin{array}{c}\phantom{\times999}167527\\\underline{\times\phantom{9999}78663}\\\phantom{\times999}502581\\\end{array}
Now multiply the first number with the 1^{st} digit in 2^{nd} number to get intermediate results. That is Multiply 167527 with 3. Write the result 502581 at the end leaving 0 spaces to the right like this.
\begin{array}{c}\phantom{\times999}167527\\\underline{\times\phantom{9999}78663}\\\phantom{\times999}502581\\\phantom{\times9}1005162\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 167527 with 6. Write the result 1005162 at the end leaving 1 spaces to the right like this.
\begin{array}{c}\phantom{\times999}167527\\\underline{\times\phantom{9999}78663}\\\phantom{\times999}502581\\\phantom{\times9}1005162\phantom{9}\\\phantom{\times}1005162\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 167527 with 6. Write the result 1005162 at the end leaving 2 spaces to the right like this.
\begin{array}{c}\phantom{\times999}167527\\\underline{\times\phantom{9999}78663}\\\phantom{\times999}502581\\\phantom{\times9}1005162\phantom{9}\\\phantom{\times}1005162\phantom{99}\\\phantom{\times}1340216\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 167527 with 8. Write the result 1340216 at the end leaving 3 spaces to the right like this.
\begin{array}{c}\phantom{\times999}167527\\\underline{\times\phantom{9999}78663}\\\phantom{\times999}502581\\\phantom{\times9}1005162\phantom{9}\\\phantom{\times}1005162\phantom{99}\\\phantom{\times}1340216\phantom{999}\\\underline{\phantom{\times}1172689\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 167527 with 7. Write the result 1172689 at the end leaving 4 spaces to the right like this.
\begin{array}{c}\phantom{\times999}167527\\\underline{\times\phantom{9999}78663}\\\phantom{\times999}502581\\\phantom{\times9}1005162\phantom{9}\\\phantom{\times}1005162\phantom{99}\\\phantom{\times}1340216\phantom{999}\\\underline{\phantom{\times}1172689\phantom{9999}}\\\phantom{\times}293274513\end{array}
Now add the intermediate results to get final answer.