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\begin{array}{c}\phantom{\times9999}289546\\\underline{\times\phantom{99}58952148}\\\end{array}
First line up the numbers vertically and match the places from the right like this.
\begin{array}{c}\phantom{\times9999}289546\\\underline{\times\phantom{99}58952148}\\\phantom{\times999}2316368\\\end{array}
Now multiply the first number with the 1^{st} digit in 2^{nd} number to get intermediate results. That is Multiply 289546 with 8. Write the result 2316368 at the end leaving 0 spaces to the right like this.
\begin{array}{c}\phantom{\times9999}289546\\\underline{\times\phantom{99}58952148}\\\phantom{\times999}2316368\\\phantom{\times99}1158184\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 289546 with 4. Write the result 1158184 at the end leaving 1 spaces to the right like this.
\begin{array}{c}\phantom{\times9999}289546\\\underline{\times\phantom{99}58952148}\\\phantom{\times999}2316368\\\phantom{\times99}1158184\phantom{9}\\\phantom{\times99}289546\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 289546 with 1. Write the result 289546 at the end leaving 2 spaces to the right like this.
\begin{array}{c}\phantom{\times9999}289546\\\underline{\times\phantom{99}58952148}\\\phantom{\times999}2316368\\\phantom{\times99}1158184\phantom{9}\\\phantom{\times99}289546\phantom{99}\\\phantom{\times9}579092\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 289546 with 2. Write the result 579092 at the end leaving 3 spaces to the right like this.
\begin{array}{c}\phantom{\times9999}289546\\\underline{\times\phantom{99}58952148}\\\phantom{\times999}2316368\\\phantom{\times99}1158184\phantom{9}\\\phantom{\times99}289546\phantom{99}\\\phantom{\times9}579092\phantom{999}\\\phantom{\times}1447730\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 289546 with 5. Write the result 1447730 at the end leaving 4 spaces to the right like this.
\begin{array}{c}\phantom{\times9999}289546\\\underline{\times\phantom{99}58952148}\\\phantom{\times999}2316368\\\phantom{\times99}1158184\phantom{9}\\\phantom{\times99}289546\phantom{99}\\\phantom{\times9}579092\phantom{999}\\\phantom{\times}1447730\phantom{9999}\\\phantom{\times}2605914\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 289546 with 9. Write the result 2605914 at the end leaving 5 spaces to the right like this.
\begin{array}{c}\phantom{\times9999}289546\\\underline{\times\phantom{99}58952148}\\\phantom{\times999}2316368\\\phantom{\times99}1158184\phantom{9}\\\phantom{\times99}289546\phantom{99}\\\phantom{\times9}579092\phantom{999}\\\phantom{\times}1447730\phantom{9999}\\\phantom{\times}2605914\phantom{99999}\\\phantom{\times}2316368\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 289546 with 8. Write the result 2316368 at the end leaving 6 spaces to the right like this.
\begin{array}{c}\phantom{\times9999}289546\\\underline{\times\phantom{99}58952148}\\\phantom{\times999}2316368\\\phantom{\times99}1158184\phantom{9}\\\phantom{\times99}289546\phantom{99}\\\phantom{\times9}579092\phantom{999}\\\phantom{\times}1447730\phantom{9999}\\\phantom{\times}2605914\phantom{99999}\\\phantom{\times}2316368\phantom{999999}\\\underline{\phantom{\times}1447730\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 289546 with 5. Write the result 1447730 at the end leaving 7 spaces to the right like this.
\begin{array}{c}\phantom{\times9999}289546\\\underline{\times\phantom{99}58952148}\\\phantom{\times999}2316368\\\phantom{\times99}1158184\phantom{9}\\\phantom{\times99}289546\phantom{99}\\\phantom{\times9}579092\phantom{999}\\\phantom{\times}1447730\phantom{9999}\\\phantom{\times}2605914\phantom{99999}\\\phantom{\times}2316368\phantom{999999}\\\underline{\phantom{\times}1447730\phantom{9999999}}\\\phantom{\times}1158610504\end{array}
Now add the intermediate results to get final answer.