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\begin{array}{c}\phantom{\times999}468\\\underline{\times\phantom{999}468}\\\end{array}
First line up the numbers vertically and match the places from the right like this.
\begin{array}{c}\phantom{\times999}468\\\underline{\times\phantom{999}468}\\\phantom{\times99}3744\\\end{array}
Now multiply the first number with the 1^{st} digit in 2^{nd} number to get intermediate results. That is Multiply 468 with 8. Write the result 3744 at the end leaving 0 spaces to the right like this.
\begin{array}{c}\phantom{\times999}468\\\underline{\times\phantom{999}468}\\\phantom{\times99}3744\\\phantom{\times9}2808\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 468 with 6. Write the result 2808 at the end leaving 1 spaces to the right like this.
\begin{array}{c}\phantom{\times999}468\\\underline{\times\phantom{999}468}\\\phantom{\times99}3744\\\phantom{\times9}2808\phantom{9}\\\underline{\phantom{\times}1872\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 468 with 4. Write the result 1872 at the end leaving 2 spaces to the right like this.
\begin{array}{c}\phantom{\times999}468\\\underline{\times\phantom{999}468}\\\phantom{\times99}3744\\\phantom{\times9}2808\phantom{9}\\\underline{\phantom{\times}1872\phantom{99}}\\\phantom{\times}219024\end{array}
Now add the intermediate results to get final answer.