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\begin{array}{c}\phantom{\times9}789456123\\\underline{\times\phantom{9999}741258}\\\end{array}
First line up the numbers vertically and match the places from the right like this.
\begin{array}{c}\phantom{\times9}789456123\\\underline{\times\phantom{9999}741258}\\\phantom{\times}2020681688\\\end{array}
Now multiply the first number with the 1^{st} digit in 2^{nd} number to get intermediate results. That is Multiply 789456123 with 8. Write the result 2020681688 at the end leaving 0 spaces to the right like this.
\begin{array}{c}\phantom{\times9}789456123\\\underline{\times\phantom{9999}741258}\\\phantom{\times}2020681688\\\phantom{\times999999999}-347686681\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 789456123 with 5. Write the result -347686681 at the end leaving 1 spaces to the right like this.
\begin{array}{c}\phantom{\times9}789456123\\\underline{\times\phantom{9999}741258}\\\phantom{\times}2020681688\\\phantom{\times999999999}-347686681\phantom{9}\\\phantom{\times}1578912246\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 789456123 with 2. Write the result 1578912246 at the end leaving 2 spaces to the right like this.
\begin{array}{c}\phantom{\times9}789456123\\\underline{\times\phantom{9999}741258}\\\phantom{\times}2020681688\\\phantom{\times999999999}-347686681\phantom{9}\\\phantom{\times}1578912246\phantom{99}\\\phantom{\times}789456123\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 789456123 with 1. Write the result 789456123 at the end leaving 3 spaces to the right like this.
\begin{array}{c}\phantom{\times9}789456123\\\underline{\times\phantom{9999}741258}\\\phantom{\times}2020681688\\\phantom{\times999999999}-347686681\phantom{9}\\\phantom{\times}1578912246\phantom{99}\\\phantom{\times}789456123\phantom{999}\\\phantom{\times999999}-1137142804\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 789456123 with 4. Write the result -1137142804 at the end leaving 4 spaces to the right like this.
\begin{array}{c}\phantom{\times9}789456123\\\underline{\times\phantom{9999}741258}\\\phantom{\times}2020681688\\\phantom{\times999999999}-347686681\phantom{9}\\\phantom{\times}1578912246\phantom{99}\\\phantom{\times}789456123\phantom{999}\\\phantom{\times999999}-1137142804\phantom{9999}\\\underline{\phantom{\times}1231225565\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 789456123 with 7. Write the result 1231225565 at the end leaving 5 spaces to the right like this.
\begin{array}{c}\phantom{\times9}789456123\\\underline{\times\phantom{9999}741258}\\\phantom{\times}2020681688\\\phantom{\times999999999}-347686681\phantom{9}\\\phantom{\times}1578912246\phantom{99}\\\phantom{\times}789456123\phantom{999}\\\phantom{\times999999}-1137142804\phantom{9999}\\\underline{\phantom{\times}1231225565\phantom{99999}}\\\phantom{\times}1372742734\end{array}
Now add the intermediate results to get final answer.