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\begin{array}{c}\phantom{\times9999}550321\\\underline{\times\phantom{999999}3254}\\\end{array}
First line up the numbers vertically and match the places from the right like this.
\begin{array}{c}\phantom{\times9999}550321\\\underline{\times\phantom{999999}3254}\\\phantom{\times999}2201284\\\end{array}
Now multiply the first number with the 1^{st} digit in 2^{nd} number to get intermediate results. That is Multiply 550321 with 4. Write the result 2201284 at the end leaving 0 spaces to the right like this.
\begin{array}{c}\phantom{\times9999}550321\\\underline{\times\phantom{999999}3254}\\\phantom{\times999}2201284\\\phantom{\times99}2751605\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 550321 with 5. Write the result 2751605 at the end leaving 1 spaces to the right like this.
\begin{array}{c}\phantom{\times9999}550321\\\underline{\times\phantom{999999}3254}\\\phantom{\times999}2201284\\\phantom{\times99}2751605\phantom{9}\\\phantom{\times9}1100642\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 550321 with 2. Write the result 1100642 at the end leaving 2 spaces to the right like this.
\begin{array}{c}\phantom{\times9999}550321\\\underline{\times\phantom{999999}3254}\\\phantom{\times999}2201284\\\phantom{\times99}2751605\phantom{9}\\\phantom{\times9}1100642\phantom{99}\\\underline{\phantom{\times}1650963\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 550321 with 3. Write the result 1650963 at the end leaving 3 spaces to the right like this.
\begin{array}{c}\phantom{\times9999}550321\\\underline{\times\phantom{999999}3254}\\\phantom{\times999}2201284\\\phantom{\times99}2751605\phantom{9}\\\phantom{\times9}1100642\phantom{99}\\\underline{\phantom{\times}1650963\phantom{999}}\\\phantom{\times}1790744534\end{array}
Now add the intermediate results to get final answer.