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\begin{array}{c}\phantom{\times999}78446\\\underline{\times\phantom{99999}538}\\\end{array}
First line up the numbers vertically and match the places from the right like this.
\begin{array}{c}\phantom{\times999}78446\\\underline{\times\phantom{99999}538}\\\phantom{\times99}627568\\\end{array}
Now multiply the first number with the 1^{st} digit in 2^{nd} number to get intermediate results. That is Multiply 78446 with 8. Write the result 627568 at the end leaving 0 spaces to the right like this.
\begin{array}{c}\phantom{\times999}78446\\\underline{\times\phantom{99999}538}\\\phantom{\times99}627568\\\phantom{\times9}235338\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 78446 with 3. Write the result 235338 at the end leaving 1 spaces to the right like this.
\begin{array}{c}\phantom{\times999}78446\\\underline{\times\phantom{99999}538}\\\phantom{\times99}627568\\\phantom{\times9}235338\phantom{9}\\\underline{\phantom{\times}392230\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 78446 with 5. Write the result 392230 at the end leaving 2 spaces to the right like this.
\begin{array}{c}\phantom{\times999}78446\\\underline{\times\phantom{99999}538}\\\phantom{\times99}627568\\\phantom{\times9}235338\phantom{9}\\\underline{\phantom{\times}392230\phantom{99}}\\\phantom{\times}42203948\end{array}
Now add the intermediate results to get final answer.