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\begin{array}{c}\phantom{\times9999}3721\\\underline{\times\phantom{9999}9316}\\\end{array}
First line up the numbers vertically and match the places from the right like this.
\begin{array}{c}\phantom{\times9999}3721\\\underline{\times\phantom{9999}9316}\\\phantom{\times999}22326\\\end{array}
Now multiply the first number with the 1^{st} digit in 2^{nd} number to get intermediate results. That is Multiply 3721 with 6. Write the result 22326 at the end leaving 0 spaces to the right like this.
\begin{array}{c}\phantom{\times9999}3721\\\underline{\times\phantom{9999}9316}\\\phantom{\times999}22326\\\phantom{\times999}3721\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 3721 with 1. Write the result 3721 at the end leaving 1 spaces to the right like this.
\begin{array}{c}\phantom{\times9999}3721\\\underline{\times\phantom{9999}9316}\\\phantom{\times999}22326\\\phantom{\times999}3721\phantom{9}\\\phantom{\times9}11163\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 3721 with 3. Write the result 11163 at the end leaving 2 spaces to the right like this.
\begin{array}{c}\phantom{\times9999}3721\\\underline{\times\phantom{9999}9316}\\\phantom{\times999}22326\\\phantom{\times999}3721\phantom{9}\\\phantom{\times9}11163\phantom{99}\\\underline{\phantom{\times}33489\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 3721 with 9. Write the result 33489 at the end leaving 3 spaces to the right like this.
\begin{array}{c}\phantom{\times9999}3721\\\underline{\times\phantom{9999}9316}\\\phantom{\times999}22326\\\phantom{\times999}3721\phantom{9}\\\phantom{\times9}11163\phantom{99}\\\underline{\phantom{\times}33489\phantom{999}}\\\phantom{\times}34664836\end{array}
Now add the intermediate results to get final answer.