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\begin{array}{c}\phantom{\times}876764\\\underline{\times\phantom{}57349}\\\end{array}
First line up the numbers vertically and match the places from the right like this.
\begin{array}{c}\phantom{\times}876764\\\underline{\times\phantom{}57349}\\\phantom{\times}7890876\\\end{array}
Now multiply the first number with the 1^{st} digit in 2^{nd} number to get intermediate results. That is Multiply 876764 with 9. Write the result 7890876 at the end leaving 0 spaces to the right like this.
\begin{array}{c}\phantom{\times}876764\\\underline{\times\phantom{}57349}\\\phantom{\times}7890876\\\phantom{\times}3507056\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 876764 with 4. Write the result 3507056 at the end leaving 1 spaces to the right like this.
\begin{array}{c}\phantom{\times}876764\\\underline{\times\phantom{}57349}\\\phantom{\times}7890876\\\phantom{\times}3507056\phantom{9}\\\phantom{\times}2630292\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 876764 with 3. Write the result 2630292 at the end leaving 2 spaces to the right like this.
\begin{array}{c}\phantom{\times}876764\\\underline{\times\phantom{}57349}\\\phantom{\times}7890876\\\phantom{\times}3507056\phantom{9}\\\phantom{\times}2630292\phantom{99}\\\phantom{\times}6137348\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 876764 with 7. Write the result 6137348 at the end leaving 3 spaces to the right like this.
\begin{array}{c}\phantom{\times}876764\\\underline{\times\phantom{}57349}\\\phantom{\times}7890876\\\phantom{\times}3507056\phantom{9}\\\phantom{\times}2630292\phantom{99}\\\phantom{\times}6137348\phantom{999}\\\underline{\phantom{\times}4383820\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 876764 with 5. Write the result 4383820 at the end leaving 4 spaces to the right like this.
\begin{array}{c}\phantom{\times}876764\\\underline{\times\phantom{}57349}\\\phantom{\times}7890876\\\phantom{\times}3507056\phantom{9}\\\phantom{\times}2630292\phantom{99}\\\phantom{\times}6137348\phantom{999}\\\underline{\phantom{\times}4383820\phantom{9999}}\\\phantom{\times}-1258068916\end{array}
Now add the intermediate results to get final answer.