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\begin{array}{c}\phantom{\times999}4637\\\underline{\times\phantom{9999}931}\\\end{array}
First line up the numbers vertically and match the places from the right like this.
\begin{array}{c}\phantom{\times999}4637\\\underline{\times\phantom{9999}931}\\\phantom{\times999}4637\\\end{array}
Now multiply the first number with the 1^{st} digit in 2^{nd} number to get intermediate results. That is Multiply 4637 with 1. Write the result 4637 at the end leaving 0 spaces to the right like this.
\begin{array}{c}\phantom{\times999}4637\\\underline{\times\phantom{9999}931}\\\phantom{\times999}4637\\\phantom{\times9}13911\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 4637 with 3. Write the result 13911 at the end leaving 1 spaces to the right like this.
\begin{array}{c}\phantom{\times999}4637\\\underline{\times\phantom{9999}931}\\\phantom{\times999}4637\\\phantom{\times9}13911\phantom{9}\\\underline{\phantom{\times}41733\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 4637 with 9. Write the result 41733 at the end leaving 2 spaces to the right like this.
\begin{array}{c}\phantom{\times999}4637\\\underline{\times\phantom{9999}931}\\\phantom{\times999}4637\\\phantom{\times9}13911\phantom{9}\\\underline{\phantom{\times}41733\phantom{99}}\\\phantom{\times}4317047\end{array}
Now add the intermediate results to get final answer.