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\begin{array}{c}\phantom{\times9}56798312\\\underline{\times\phantom{99999}9765}\\\end{array}
First line up the numbers vertically and match the places from the right like this.
\begin{array}{c}\phantom{\times9}56798312\\\underline{\times\phantom{99999}9765}\\\phantom{\times}283991560\\\end{array}
Now multiply the first number with the 1^{st} digit in 2^{nd} number to get intermediate results. That is Multiply 56798312 with 5. Write the result 283991560 at the end leaving 0 spaces to the right like this.
\begin{array}{c}\phantom{\times9}56798312\\\underline{\times\phantom{99999}9765}\\\phantom{\times}283991560\\\phantom{\times}340789872\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 56798312 with 6. Write the result 340789872 at the end leaving 1 spaces to the right like this.
\begin{array}{c}\phantom{\times9}56798312\\\underline{\times\phantom{99999}9765}\\\phantom{\times}283991560\\\phantom{\times}340789872\phantom{9}\\\phantom{\times}397588184\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 56798312 with 7. Write the result 397588184 at the end leaving 2 spaces to the right like this.
\begin{array}{c}\phantom{\times9}56798312\\\underline{\times\phantom{99999}9765}\\\phantom{\times}283991560\\\phantom{\times}340789872\phantom{9}\\\phantom{\times}397588184\phantom{99}\\\underline{\phantom{\times}511184808\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 56798312 with 9. Write the result 511184808 at the end leaving 3 spaces to the right like this.
\begin{array}{c}\phantom{\times9}56798312\\\underline{\times\phantom{99999}9765}\\\phantom{\times}283991560\\\phantom{\times}340789872\phantom{9}\\\phantom{\times}397588184\phantom{99}\\\underline{\phantom{\times}511184808\phantom{999}}\\\phantom{\times}584735496\end{array}
Now add the intermediate results to get final answer.