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\begin{array}{c}\phantom{\times9}506781230\\\underline{\times\phantom{99999}27768}\\\end{array}
First line up the numbers vertically and match the places from the right like this.
\begin{array}{c}\phantom{\times9}506781230\\\underline{\times\phantom{99999}27768}\\\phantom{\times9999999999}-240717456\\\end{array}
Now multiply the first number with the 1^{st} digit in 2^{nd} number to get intermediate results. That is Multiply 506781230 with 8. Write the result -240717456 at the end leaving 0 spaces to the right like this.
\begin{array}{c}\phantom{\times9}506781230\\\underline{\times\phantom{99999}27768}\\\phantom{\times9999999999}-240717456\\\phantom{\times999999999}-1254279916\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 506781230 with 6. Write the result -1254279916 at the end leaving 1 spaces to the right like this.
\begin{array}{c}\phantom{\times9}506781230\\\underline{\times\phantom{99999}27768}\\\phantom{\times9999999999}-240717456\\\phantom{\times999999999}-1254279916\phantom{9}\\\phantom{\times99999999}-747498686\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 506781230 with 7. Write the result -747498686 at the end leaving 2 spaces to the right like this.
\begin{array}{c}\phantom{\times9}506781230\\\underline{\times\phantom{99999}27768}\\\phantom{\times9999999999}-240717456\\\phantom{\times999999999}-1254279916\phantom{9}\\\phantom{\times99999999}-747498686\phantom{99}\\\phantom{\times9999999}-747498686\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 506781230 with 7. Write the result -747498686 at the end leaving 3 spaces to the right like this.
\begin{array}{c}\phantom{\times9}506781230\\\underline{\times\phantom{99999}27768}\\\phantom{\times9999999999}-240717456\\\phantom{\times999999999}-1254279916\phantom{9}\\\phantom{\times99999999}-747498686\phantom{99}\\\phantom{\times9999999}-747498686\phantom{999}\\\underline{\phantom{\times}1013562460\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 506781230 with 2. Write the result 1013562460 at the end leaving 4 spaces to the right like this.
\begin{array}{c}\phantom{\times9}506781230\\\underline{\times\phantom{99999}27768}\\\phantom{\times9999999999}-240717456\\\phantom{\times999999999}-1254279916\phantom{9}\\\phantom{\times99999999}-747498686\phantom{99}\\\phantom{\times9999999}-747498686\phantom{999}\\\underline{\phantom{\times}1013562460\phantom{9999}}\\\phantom{\times}1988332944\end{array}
Now add the intermediate results to get final answer.