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\begin{array}{c}\phantom{\times}598797209\\\underline{\times\phantom{9999999}87}\\\end{array}
First line up the numbers vertically and match the places from the right like this.
\begin{array}{c}\phantom{\times}598797209\\\underline{\times\phantom{9999999}87}\\\phantom{\times999999999}-103386833\\\end{array}
Now multiply the first number with the 1^{st} digit in 2^{nd} number to get intermediate results. That is Multiply 598797209 with 7. Write the result -103386833 at the end leaving 0 spaces to the right like this.
\begin{array}{c}\phantom{\times}598797209\\\underline{\times\phantom{9999999}87}\\\phantom{\times999999999}-103386833\\\underline{\phantom{\times}495410376\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 598797209 with 8. Write the result 495410376 at the end leaving 1 spaces to the right like this.
\begin{array}{c}\phantom{\times}598797209\\\underline{\times\phantom{9999999}87}\\\phantom{\times999999999}-103386833\\\underline{\phantom{\times}495410376\phantom{9}}\\\phantom{\times}555749631\end{array}
Now add the intermediate results to get final answer.