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\begin{array}{c}\phantom{\times9}123456789\\\underline{\times\phantom{9999999}810}\\\end{array}
First line up the numbers vertically and match the places from the right like this.
\begin{array}{c}\phantom{\times9}123456789\\\underline{\times\phantom{9999999}810}\\\phantom{\times9999999999}0\\\end{array}
Now multiply the first number with the 1^{st} digit in 2^{nd} number to get intermediate results. That is Multiply 123456789 with 0. Write the result 0 at the end leaving 0 spaces to the right like this.
\begin{array}{c}\phantom{\times9}123456789\\\underline{\times\phantom{9999999}810}\\\phantom{\times9999999999}0\\\phantom{\times}123456789\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 123456789 with 1. Write the result 123456789 at the end leaving 1 spaces to the right like this.
\begin{array}{c}\phantom{\times9}123456789\\\underline{\times\phantom{9999999}810}\\\phantom{\times9999999999}0\\\phantom{\times}123456789\phantom{9}\\\underline{\phantom{\times}987654312\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 123456789 with 8. Write the result 987654312 at the end leaving 2 spaces to the right like this.
\begin{array}{c}\phantom{\times9}123456789\\\underline{\times\phantom{9999999}810}\\\phantom{\times9999999999}0\\\phantom{\times}123456789\phantom{9}\\\underline{\phantom{\times}987654312\phantom{99}}\\\phantom{\times}1215751282\end{array}
Now add the intermediate results to get final answer.