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\begin{array}{c}\phantom{\times99999}2496\\\underline{\times\phantom{9999}54781}\\\end{array}
First line up the numbers vertically and match the places from the right like this.
\begin{array}{c}\phantom{\times99999}2496\\\underline{\times\phantom{9999}54781}\\\phantom{\times99999}2496\\\end{array}
Now multiply the first number with the 1^{st} digit in 2^{nd} number to get intermediate results. That is Multiply 2496 with 1. Write the result 2496 at the end leaving 0 spaces to the right like this.
\begin{array}{c}\phantom{\times99999}2496\\\underline{\times\phantom{9999}54781}\\\phantom{\times99999}2496\\\phantom{\times999}19968\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 2496 with 8. Write the result 19968 at the end leaving 1 spaces to the right like this.
\begin{array}{c}\phantom{\times99999}2496\\\underline{\times\phantom{9999}54781}\\\phantom{\times99999}2496\\\phantom{\times999}19968\phantom{9}\\\phantom{\times99}17472\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 2496 with 7. Write the result 17472 at the end leaving 2 spaces to the right like this.
\begin{array}{c}\phantom{\times99999}2496\\\underline{\times\phantom{9999}54781}\\\phantom{\times99999}2496\\\phantom{\times999}19968\phantom{9}\\\phantom{\times99}17472\phantom{99}\\\phantom{\times99}9984\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 2496 with 4. Write the result 9984 at the end leaving 3 spaces to the right like this.
\begin{array}{c}\phantom{\times99999}2496\\\underline{\times\phantom{9999}54781}\\\phantom{\times99999}2496\\\phantom{\times999}19968\phantom{9}\\\phantom{\times99}17472\phantom{99}\\\phantom{\times99}9984\phantom{999}\\\underline{\phantom{\times}12480\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 2496 with 5. Write the result 12480 at the end leaving 4 spaces to the right like this.
\begin{array}{c}\phantom{\times99999}2496\\\underline{\times\phantom{9999}54781}\\\phantom{\times99999}2496\\\phantom{\times999}19968\phantom{9}\\\phantom{\times99}17472\phantom{99}\\\phantom{\times99}9984\phantom{999}\\\underline{\phantom{\times}12480\phantom{9999}}\\\phantom{\times}136733376\end{array}
Now add the intermediate results to get final answer.