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\begin{array}{c}\phantom{\times99999}981\\\underline{\times\phantom{999}84472}\\\end{array}
First line up the numbers vertically and match the places from the right like this.
\begin{array}{c}\phantom{\times99999}981\\\underline{\times\phantom{999}84472}\\\phantom{\times9999}1962\\\end{array}
Now multiply the first number with the 1^{st} digit in 2^{nd} number to get intermediate results. That is Multiply 981 with 2. Write the result 1962 at the end leaving 0 spaces to the right like this.
\begin{array}{c}\phantom{\times99999}981\\\underline{\times\phantom{999}84472}\\\phantom{\times9999}1962\\\phantom{\times999}6867\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 981 with 7. Write the result 6867 at the end leaving 1 spaces to the right like this.
\begin{array}{c}\phantom{\times99999}981\\\underline{\times\phantom{999}84472}\\\phantom{\times9999}1962\\\phantom{\times999}6867\phantom{9}\\\phantom{\times99}3924\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 981 with 4. Write the result 3924 at the end leaving 2 spaces to the right like this.
\begin{array}{c}\phantom{\times99999}981\\\underline{\times\phantom{999}84472}\\\phantom{\times9999}1962\\\phantom{\times999}6867\phantom{9}\\\phantom{\times99}3924\phantom{99}\\\phantom{\times9}3924\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 981 with 4. Write the result 3924 at the end leaving 3 spaces to the right like this.
\begin{array}{c}\phantom{\times99999}981\\\underline{\times\phantom{999}84472}\\\phantom{\times9999}1962\\\phantom{\times999}6867\phantom{9}\\\phantom{\times99}3924\phantom{99}\\\phantom{\times9}3924\phantom{999}\\\underline{\phantom{\times}7848\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 981 with 8. Write the result 7848 at the end leaving 4 spaces to the right like this.
\begin{array}{c}\phantom{\times99999}981\\\underline{\times\phantom{999}84472}\\\phantom{\times9999}1962\\\phantom{\times999}6867\phantom{9}\\\phantom{\times99}3924\phantom{99}\\\phantom{\times9}3924\phantom{999}\\\underline{\phantom{\times}7848\phantom{9999}}\\\phantom{\times}82867032\end{array}
Now add the intermediate results to get final answer.