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\begin{array}{c}\phantom{\times}547876094\\\underline{\times\phantom{999}589007}\\\end{array}
First line up the numbers vertically and match the places from the right like this.
\begin{array}{c}\phantom{\times}547876094\\\underline{\times\phantom{999}589007}\\\phantom{\times999999999}-459834638\\\end{array}
Now multiply the first number with the 1^{st} digit in 2^{nd} number to get intermediate results. That is Multiply 547876094 with 7. Write the result -459834638 at the end leaving 0 spaces to the right like this.
\begin{array}{c}\phantom{\times}547876094\\\underline{\times\phantom{999}589007}\\\phantom{\times999999999}-459834638\\\phantom{\times99999999}0\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 547876094 with 0. Write the result 0 at the end leaving 1 spaces to the right like this.
\begin{array}{c}\phantom{\times}547876094\\\underline{\times\phantom{999}589007}\\\phantom{\times999999999}-459834638\\\phantom{\times99999999}0\phantom{9}\\\phantom{\times9999999}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 547876094 with 0. Write the result 0 at the end leaving 2 spaces to the right like this.
\begin{array}{c}\phantom{\times}547876094\\\underline{\times\phantom{999}589007}\\\phantom{\times999999999}-459834638\\\phantom{\times99999999}0\phantom{9}\\\phantom{\times9999999}0\phantom{99}\\\phantom{\times}635917550\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 547876094 with 9. Write the result 635917550 at the end leaving 3 spaces to the right like this.
\begin{array}{c}\phantom{\times}547876094\\\underline{\times\phantom{999}589007}\\\phantom{\times999999999}-459834638\\\phantom{\times99999999}0\phantom{9}\\\phantom{\times9999999}0\phantom{99}\\\phantom{\times}635917550\phantom{999}\\\phantom{\times}88041456\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 547876094 with 8. Write the result 88041456 at the end leaving 4 spaces to the right like this.
\begin{array}{c}\phantom{\times}547876094\\\underline{\times\phantom{999}589007}\\\phantom{\times999999999}-459834638\\\phantom{\times99999999}0\phantom{9}\\\phantom{\times9999999}0\phantom{99}\\\phantom{\times}635917550\phantom{999}\\\phantom{\times}88041456\phantom{9999}\\\underline{\phantom{\times9999}-1555586826\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 547876094 with 5. Write the result -1555586826 at the end leaving 5 spaces to the right like this.
\begin{array}{c}\phantom{\times}547876094\\\underline{\times\phantom{999}589007}\\\phantom{\times999999999}-459834638\\\phantom{\times99999999}0\phantom{9}\\\phantom{\times9999999}0\phantom{99}\\\phantom{\times}635917550\phantom{999}\\\phantom{\times}88041456\phantom{9999}\\\underline{\phantom{\times9999}-1555586826\phantom{99999}}\\\phantom{\times}486713698\end{array}
Now add the intermediate results to get final answer.