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\begin{array}{c}\phantom{\times999}183165\\\underline{\times\phantom{9999}28263}\\\end{array}
First line up the numbers vertically and match the places from the right like this.
\begin{array}{c}\phantom{\times999}183165\\\underline{\times\phantom{9999}28263}\\\phantom{\times999}549495\\\end{array}
Now multiply the first number with the 1^{st} digit in 2^{nd} number to get intermediate results. That is Multiply 183165 with 3. Write the result 549495 at the end leaving 0 spaces to the right like this.
\begin{array}{c}\phantom{\times999}183165\\\underline{\times\phantom{9999}28263}\\\phantom{\times999}549495\\\phantom{\times9}1098990\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 183165 with 6. Write the result 1098990 at the end leaving 1 spaces to the right like this.
\begin{array}{c}\phantom{\times999}183165\\\underline{\times\phantom{9999}28263}\\\phantom{\times999}549495\\\phantom{\times9}1098990\phantom{9}\\\phantom{\times9}366330\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 183165 with 2. Write the result 366330 at the end leaving 2 spaces to the right like this.
\begin{array}{c}\phantom{\times999}183165\\\underline{\times\phantom{9999}28263}\\\phantom{\times999}549495\\\phantom{\times9}1098990\phantom{9}\\\phantom{\times9}366330\phantom{99}\\\phantom{\times}1465320\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 183165 with 8. Write the result 1465320 at the end leaving 3 spaces to the right like this.
\begin{array}{c}\phantom{\times999}183165\\\underline{\times\phantom{9999}28263}\\\phantom{\times999}549495\\\phantom{\times9}1098990\phantom{9}\\\phantom{\times9}366330\phantom{99}\\\phantom{\times}1465320\phantom{999}\\\underline{\phantom{\times}366330\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 183165 with 2. Write the result 366330 at the end leaving 4 spaces to the right like this.
\begin{array}{c}\phantom{\times999}183165\\\underline{\times\phantom{9999}28263}\\\phantom{\times999}549495\\\phantom{\times9}1098990\phantom{9}\\\phantom{\times9}366330\phantom{99}\\\phantom{\times}1465320\phantom{999}\\\underline{\phantom{\times}366330\phantom{9999}}\\\phantom{\times}881825099\end{array}
Now add the intermediate results to get final answer.