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\begin{array}{c}\phantom{\times9}300\\\underline{\times\phantom{99}25}\\\end{array}
First line up the numbers vertically and match the places from the right like this.
\begin{array}{c}\phantom{\times9}300\\\underline{\times\phantom{99}25}\\\phantom{\times}1500\\\end{array}
Now multiply the first number with the 1^{st} digit in 2^{nd} number to get intermediate results. That is Multiply 300 with 5. Write the result 1500 at the end leaving 0 spaces to the right like this.
\begin{array}{c}\phantom{\times9}300\\\underline{\times\phantom{99}25}\\\phantom{\times}1500\\\underline{\phantom{\times}600\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 300 with 2. Write the result 600 at the end leaving 1 spaces to the right like this.
\begin{array}{c}\phantom{\times9}300\\\underline{\times\phantom{99}25}\\\phantom{\times}1500\\\underline{\phantom{\times}600\phantom{9}}\\\phantom{\times}7500\end{array}
Now add the intermediate results to get final answer.