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\begin{array}{c}\phantom{\times999}360\\\underline{\times\phantom{999}480}\\\end{array}
First line up the numbers vertically and match the places from the right like this.
\begin{array}{c}\phantom{\times999}360\\\underline{\times\phantom{999}480}\\\phantom{\times999999}0\\\end{array}
Now multiply the first number with the 1^{st} digit in 2^{nd} number to get intermediate results. That is Multiply 360 with 0. Write the result 0 at the end leaving 0 spaces to the right like this.
\begin{array}{c}\phantom{\times999}360\\\underline{\times\phantom{999}480}\\\phantom{\times999999}0\\\phantom{\times9}2880\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 360 with 8. Write the result 2880 at the end leaving 1 spaces to the right like this.
\begin{array}{c}\phantom{\times999}360\\\underline{\times\phantom{999}480}\\\phantom{\times999999}0\\\phantom{\times9}2880\phantom{9}\\\underline{\phantom{\times}1440\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 360 with 4. Write the result 1440 at the end leaving 2 spaces to the right like this.
\begin{array}{c}\phantom{\times999}360\\\underline{\times\phantom{999}480}\\\phantom{\times999999}0\\\phantom{\times9}2880\phantom{9}\\\underline{\phantom{\times}1440\phantom{99}}\\\phantom{\times}172800\end{array}
Now add the intermediate results to get final answer.