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\begin{array}{c}\phantom{\times9999}503\\\underline{\times\phantom{99}10231}\\\end{array}
First line up the numbers vertically and match the places from the right like this.
\begin{array}{c}\phantom{\times9999}503\\\underline{\times\phantom{99}10231}\\\phantom{\times9999}503\\\end{array}
Now multiply the first number with the 1^{st} digit in 2^{nd} number to get intermediate results. That is Multiply 503 with 1. Write the result 503 at the end leaving 0 spaces to the right like this.
\begin{array}{c}\phantom{\times9999}503\\\underline{\times\phantom{99}10231}\\\phantom{\times9999}503\\\phantom{\times99}1509\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 503 with 3. Write the result 1509 at the end leaving 1 spaces to the right like this.
\begin{array}{c}\phantom{\times9999}503\\\underline{\times\phantom{99}10231}\\\phantom{\times9999}503\\\phantom{\times99}1509\phantom{9}\\\phantom{\times9}1006\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 503 with 2. Write the result 1006 at the end leaving 2 spaces to the right like this.
\begin{array}{c}\phantom{\times9999}503\\\underline{\times\phantom{99}10231}\\\phantom{\times9999}503\\\phantom{\times99}1509\phantom{9}\\\phantom{\times9}1006\phantom{99}\\\phantom{\times9999}0\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 503 with 0. Write the result 0 at the end leaving 3 spaces to the right like this.
\begin{array}{c}\phantom{\times9999}503\\\underline{\times\phantom{99}10231}\\\phantom{\times9999}503\\\phantom{\times99}1509\phantom{9}\\\phantom{\times9}1006\phantom{99}\\\phantom{\times9999}0\phantom{999}\\\underline{\phantom{\times}503\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 503 with 1. Write the result 503 at the end leaving 4 spaces to the right like this.
\begin{array}{c}\phantom{\times9999}503\\\underline{\times\phantom{99}10231}\\\phantom{\times9999}503\\\phantom{\times99}1509\phantom{9}\\\phantom{\times9}1006\phantom{99}\\\phantom{\times9999}0\phantom{999}\\\underline{\phantom{\times}503\phantom{9999}}\\\phantom{\times}5146193\end{array}
Now add the intermediate results to get final answer.