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\begin{array}{c}\phantom{\times999}396\\\underline{\times\phantom{999}824}\\\end{array}
First line up the numbers vertically and match the places from the right like this.
\begin{array}{c}\phantom{\times999}396\\\underline{\times\phantom{999}824}\\\phantom{\times99}1584\\\end{array}
Now multiply the first number with the 1^{st} digit in 2^{nd} number to get intermediate results. That is Multiply 396 with 4. Write the result 1584 at the end leaving 0 spaces to the right like this.
\begin{array}{c}\phantom{\times999}396\\\underline{\times\phantom{999}824}\\\phantom{\times99}1584\\\phantom{\times99}792\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 396 with 2. Write the result 792 at the end leaving 1 spaces to the right like this.
\begin{array}{c}\phantom{\times999}396\\\underline{\times\phantom{999}824}\\\phantom{\times99}1584\\\phantom{\times99}792\phantom{9}\\\underline{\phantom{\times}3168\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 396 with 8. Write the result 3168 at the end leaving 2 spaces to the right like this.
\begin{array}{c}\phantom{\times999}396\\\underline{\times\phantom{999}824}\\\phantom{\times99}1584\\\phantom{\times99}792\phantom{9}\\\underline{\phantom{\times}3168\phantom{99}}\\\phantom{\times}326304\end{array}
Now add the intermediate results to get final answer.