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\begin{array}{c}\phantom{\times}123456789\\\underline{\times\phantom{}12345678}\\\end{array}
First line up the numbers vertically and match the places from the right like this.
\begin{array}{c}\phantom{\times}123456789\\\underline{\times\phantom{}12345678}\\\phantom{\times}987654312\\\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 8. Write the result 987654312 at the end leaving 0 spaces to the right like this.
\begin{array}{c}\phantom{\times}123456789\\\underline{\times\phantom{}12345678}\\\phantom{\times}987654312\\\phantom{\times}864197523\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 7. Write the result 864197523 at the end leaving 1 spaces to the right like this.
\begin{array}{c}\phantom{\times}123456789\\\underline{\times\phantom{}12345678}\\\phantom{\times}987654312\\\phantom{\times}864197523\phantom{9}\\\phantom{\times}740740734\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 6. Write the result 740740734 at the end leaving 2 spaces to the right like this.
\begin{array}{c}\phantom{\times}123456789\\\underline{\times\phantom{}12345678}\\\phantom{\times}987654312\\\phantom{\times}864197523\phantom{9}\\\phantom{\times}740740734\phantom{99}\\\phantom{\times}617283945\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 123456789 with 5. Write the result 617283945 at the end leaving 3 spaces to the right like this.
\begin{array}{c}\phantom{\times}123456789\\\underline{\times\phantom{}12345678}\\\phantom{\times}987654312\\\phantom{\times}864197523\phantom{9}\\\phantom{\times}740740734\phantom{99}\\\phantom{\times}617283945\phantom{999}\\\phantom{\times}493827156\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 123456789 with 4. Write the result 493827156 at the end leaving 4 spaces to the right like this.
\begin{array}{c}\phantom{\times}123456789\\\underline{\times\phantom{}12345678}\\\phantom{\times}987654312\\\phantom{\times}864197523\phantom{9}\\\phantom{\times}740740734\phantom{99}\\\phantom{\times}617283945\phantom{999}\\\phantom{\times}493827156\phantom{9999}\\\phantom{\times}370370367\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 123456789 with 3. Write the result 370370367 at the end leaving 5 spaces to the right like this.
\begin{array}{c}\phantom{\times}123456789\\\underline{\times\phantom{}12345678}\\\phantom{\times}987654312\\\phantom{\times}864197523\phantom{9}\\\phantom{\times}740740734\phantom{99}\\\phantom{\times}617283945\phantom{999}\\\phantom{\times}493827156\phantom{9999}\\\phantom{\times}370370367\phantom{99999}\\\phantom{\times}246913578\phantom{999999}\\\end{array}
Now multiply the first number with the 7^{th} digit in 2^{nd} number to get intermediate results. That is Multiply 123456789 with 2. Write the result 246913578 at the end leaving 6 spaces to the right like this.
\begin{array}{c}\phantom{\times}123456789\\\underline{\times\phantom{}12345678}\\\phantom{\times}987654312\\\phantom{\times}864197523\phantom{9}\\\phantom{\times}740740734\phantom{99}\\\phantom{\times}617283945\phantom{999}\\\phantom{\times}493827156\phantom{9999}\\\phantom{\times}370370367\phantom{99999}\\\phantom{\times}246913578\phantom{999999}\\\underline{\phantom{\times}123456789\phantom{9999999}}\\\end{array}
Now multiply the first number with the 8^{th} digit in 2^{nd} number to get intermediate results. That is Multiply 123456789 with 1. Write the result 123456789 at the end leaving 7 spaces to the right like this.
\begin{array}{c}\phantom{\times}123456789\\\underline{\times\phantom{}12345678}\\\phantom{\times}987654312\\\phantom{\times}864197523\phantom{9}\\\phantom{\times}740740734\phantom{99}\\\phantom{\times}617283945\phantom{999}\\\phantom{\times}493827156\phantom{9999}\\\phantom{\times}370370367\phantom{99999}\\\phantom{\times}246913578\phantom{999999}\\\underline{\phantom{\times}123456789\phantom{9999999}}\\\phantom{\times}-1575390874\end{array}
Now add the intermediate results to get final answer.