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\begin{array}{c}\phantom{\times99999}64567\\\underline{\times\phantom{99999}32287}\\\end{array}
First line up the numbers vertically and match the places from the right like this.
\begin{array}{c}\phantom{\times99999}64567\\\underline{\times\phantom{99999}32287}\\\phantom{\times9999}451969\\\end{array}
Now multiply the first number with the 1^{st} digit in 2^{nd} number to get intermediate results. That is Multiply 64567 with 7. Write the result 451969 at the end leaving 0 spaces to the right like this.
\begin{array}{c}\phantom{\times99999}64567\\\underline{\times\phantom{99999}32287}\\\phantom{\times9999}451969\\\phantom{\times999}516536\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 64567 with 8. Write the result 516536 at the end leaving 1 spaces to the right like this.
\begin{array}{c}\phantom{\times99999}64567\\\underline{\times\phantom{99999}32287}\\\phantom{\times9999}451969\\\phantom{\times999}516536\phantom{9}\\\phantom{\times99}129134\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 64567 with 2. Write the result 129134 at the end leaving 2 spaces to the right like this.
\begin{array}{c}\phantom{\times99999}64567\\\underline{\times\phantom{99999}32287}\\\phantom{\times9999}451969\\\phantom{\times999}516536\phantom{9}\\\phantom{\times99}129134\phantom{99}\\\phantom{\times9}129134\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 64567 with 2. Write the result 129134 at the end leaving 3 spaces to the right like this.
\begin{array}{c}\phantom{\times99999}64567\\\underline{\times\phantom{99999}32287}\\\phantom{\times9999}451969\\\phantom{\times999}516536\phantom{9}\\\phantom{\times99}129134\phantom{99}\\\phantom{\times9}129134\phantom{999}\\\underline{\phantom{\times}193701\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 64567 with 3. Write the result 193701 at the end leaving 4 spaces to the right like this.
\begin{array}{c}\phantom{\times99999}64567\\\underline{\times\phantom{99999}32287}\\\phantom{\times9999}451969\\\phantom{\times999}516536\phantom{9}\\\phantom{\times99}129134\phantom{99}\\\phantom{\times9}129134\phantom{999}\\\underline{\phantom{\times}193701\phantom{9999}}\\\phantom{\times}2084674729\end{array}
Now add the intermediate results to get final answer.