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\begin{array}{c}\phantom{\times99999}2589\\\underline{\times\phantom{9999}86231}\\\end{array}
First line up the numbers vertically and match the places from the right like this.
\begin{array}{c}\phantom{\times99999}2589\\\underline{\times\phantom{9999}86231}\\\phantom{\times99999}2589\\\end{array}
Now multiply the first number with the 1^{st} digit in 2^{nd} number to get intermediate results. That is Multiply 2589 with 1. Write the result 2589 at the end leaving 0 spaces to the right like this.
\begin{array}{c}\phantom{\times99999}2589\\\underline{\times\phantom{9999}86231}\\\phantom{\times99999}2589\\\phantom{\times9999}7767\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 2589 with 3. Write the result 7767 at the end leaving 1 spaces to the right like this.
\begin{array}{c}\phantom{\times99999}2589\\\underline{\times\phantom{9999}86231}\\\phantom{\times99999}2589\\\phantom{\times9999}7767\phantom{9}\\\phantom{\times999}5178\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 2589 with 2. Write the result 5178 at the end leaving 2 spaces to the right like this.
\begin{array}{c}\phantom{\times99999}2589\\\underline{\times\phantom{9999}86231}\\\phantom{\times99999}2589\\\phantom{\times9999}7767\phantom{9}\\\phantom{\times999}5178\phantom{99}\\\phantom{\times9}15534\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 2589 with 6. Write the result 15534 at the end leaving 3 spaces to the right like this.
\begin{array}{c}\phantom{\times99999}2589\\\underline{\times\phantom{9999}86231}\\\phantom{\times99999}2589\\\phantom{\times9999}7767\phantom{9}\\\phantom{\times999}5178\phantom{99}\\\phantom{\times9}15534\phantom{999}\\\underline{\phantom{\times}20712\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 2589 with 8. Write the result 20712 at the end leaving 4 spaces to the right like this.
\begin{array}{c}\phantom{\times99999}2589\\\underline{\times\phantom{9999}86231}\\\phantom{\times99999}2589\\\phantom{\times9999}7767\phantom{9}\\\phantom{\times999}5178\phantom{99}\\\phantom{\times9}15534\phantom{999}\\\underline{\phantom{\times}20712\phantom{9999}}\\\phantom{\times}223252059\end{array}
Now add the intermediate results to get final answer.