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\begin{array}{c}\phantom{\times}893702\\\underline{\times\phantom{}509087}\\\end{array}
First line up the numbers vertically and match the places from the right like this.
\begin{array}{c}\phantom{\times}893702\\\underline{\times\phantom{}509087}\\\phantom{\times}6255914\\\end{array}
Now multiply the first number with the 1^{st} digit in 2^{nd} number to get intermediate results. That is Multiply 893702 with 7. Write the result 6255914 at the end leaving 0 spaces to the right like this.
\begin{array}{c}\phantom{\times}893702\\\underline{\times\phantom{}509087}\\\phantom{\times}6255914\\\phantom{\times}7149616\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 893702 with 8. Write the result 7149616 at the end leaving 1 spaces to the right like this.
\begin{array}{c}\phantom{\times}893702\\\underline{\times\phantom{}509087}\\\phantom{\times}6255914\\\phantom{\times}7149616\phantom{9}\\\phantom{\times}0\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 893702 with 0. Write the result 0 at the end leaving 2 spaces to the right like this.
\begin{array}{c}\phantom{\times}893702\\\underline{\times\phantom{}509087}\\\phantom{\times}6255914\\\phantom{\times}7149616\phantom{9}\\\phantom{\times}0\phantom{99}\\\phantom{\times}8043318\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 893702 with 9. Write the result 8043318 at the end leaving 3 spaces to the right like this.
\begin{array}{c}\phantom{\times}893702\\\underline{\times\phantom{}509087}\\\phantom{\times}6255914\\\phantom{\times}7149616\phantom{9}\\\phantom{\times}0\phantom{99}\\\phantom{\times}8043318\phantom{999}\\\phantom{\times}0\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 893702 with 0. Write the result 0 at the end leaving 4 spaces to the right like this.
\begin{array}{c}\phantom{\times}893702\\\underline{\times\phantom{}509087}\\\phantom{\times}6255914\\\phantom{\times}7149616\phantom{9}\\\phantom{\times}0\phantom{99}\\\phantom{\times}8043318\phantom{999}\\\phantom{\times}0\phantom{9999}\\\underline{\phantom{\times}4468510\phantom{99999}}\\\end{array}
Now multiply the first number with the 6^{th} digit in 2^{nd} number to get intermediate results. That is Multiply 893702 with 5. Write the result 4468510 at the end leaving 5 spaces to the right like this.
\begin{array}{c}\phantom{\times}893702\\\underline{\times\phantom{}509087}\\\phantom{\times}6255914\\\phantom{\times}7149616\phantom{9}\\\phantom{\times}0\phantom{99}\\\phantom{\times}8043318\phantom{999}\\\phantom{\times}0\phantom{9999}\\\underline{\phantom{\times}4468510\phantom{99999}}\\\phantom{\times}-294463302\end{array}
Now add the intermediate results to get final answer.