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\begin{array}{c}\phantom{\times9999}544\\\underline{\times\phantom{999}9978}\\\end{array}
First line up the numbers vertically and match the places from the right like this.
\begin{array}{c}\phantom{\times9999}544\\\underline{\times\phantom{999}9978}\\\phantom{\times999}4352\\\end{array}
Now multiply the first number with the 1^{st} digit in 2^{nd} number to get intermediate results. That is Multiply 544 with 8. Write the result 4352 at the end leaving 0 spaces to the right like this.
\begin{array}{c}\phantom{\times9999}544\\\underline{\times\phantom{999}9978}\\\phantom{\times999}4352\\\phantom{\times99}3808\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 544 with 7. Write the result 3808 at the end leaving 1 spaces to the right like this.
\begin{array}{c}\phantom{\times9999}544\\\underline{\times\phantom{999}9978}\\\phantom{\times999}4352\\\phantom{\times99}3808\phantom{9}\\\phantom{\times9}4896\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 544 with 9. Write the result 4896 at the end leaving 2 spaces to the right like this.
\begin{array}{c}\phantom{\times9999}544\\\underline{\times\phantom{999}9978}\\\phantom{\times999}4352\\\phantom{\times99}3808\phantom{9}\\\phantom{\times9}4896\phantom{99}\\\underline{\phantom{\times}4896\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 544 with 9. Write the result 4896 at the end leaving 3 spaces to the right like this.
\begin{array}{c}\phantom{\times9999}544\\\underline{\times\phantom{999}9978}\\\phantom{\times999}4352\\\phantom{\times99}3808\phantom{9}\\\phantom{\times9}4896\phantom{99}\\\underline{\phantom{\times}4896\phantom{999}}\\\phantom{\times}5428032\end{array}
Now add the intermediate results to get final answer.