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\begin{array}{c}\phantom{\times99999}15\\\underline{\times\phantom{9}325897}\\\end{array}
First line up the numbers vertically and match the places from the right like this.
\begin{array}{c}\phantom{\times99999}15\\\underline{\times\phantom{9}325897}\\\phantom{\times9999}105\\\end{array}
Now multiply the first number with the 1^{st} digit in 2^{nd} number to get intermediate results. That is Multiply 15 with 7. Write the result 105 at the end leaving 0 spaces to the right like this.
\begin{array}{c}\phantom{\times99999}15\\\underline{\times\phantom{9}325897}\\\phantom{\times9999}105\\\phantom{\times999}135\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 15 with 9. Write the result 135 at the end leaving 1 spaces to the right like this.
\begin{array}{c}\phantom{\times99999}15\\\underline{\times\phantom{9}325897}\\\phantom{\times9999}105\\\phantom{\times999}135\phantom{9}\\\phantom{\times99}120\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 15 with 8. Write the result 120 at the end leaving 2 spaces to the right like this.
\begin{array}{c}\phantom{\times99999}15\\\underline{\times\phantom{9}325897}\\\phantom{\times9999}105\\\phantom{\times999}135\phantom{9}\\\phantom{\times99}120\phantom{99}\\\phantom{\times99}75\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 15 with 5. Write the result 75 at the end leaving 3 spaces to the right like this.
\begin{array}{c}\phantom{\times99999}15\\\underline{\times\phantom{9}325897}\\\phantom{\times9999}105\\\phantom{\times999}135\phantom{9}\\\phantom{\times99}120\phantom{99}\\\phantom{\times99}75\phantom{999}\\\phantom{\times9}30\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 15 with 2. Write the result 30 at the end leaving 4 spaces to the right like this.
\begin{array}{c}\phantom{\times99999}15\\\underline{\times\phantom{9}325897}\\\phantom{\times9999}105\\\phantom{\times999}135\phantom{9}\\\phantom{\times99}120\phantom{99}\\\phantom{\times99}75\phantom{999}\\\phantom{\times9}30\phantom{9999}\\\underline{\phantom{\times}45\phantom{99999}}\\\end{array}
Now multiply the first number with the 6^{th} digit in 2^{nd} number to get intermediate results. That is Multiply 15 with 3. Write the result 45 at the end leaving 5 spaces to the right like this.
\begin{array}{c}\phantom{\times99999}15\\\underline{\times\phantom{9}325897}\\\phantom{\times9999}105\\\phantom{\times999}135\phantom{9}\\\phantom{\times99}120\phantom{99}\\\phantom{\times99}75\phantom{999}\\\phantom{\times9}30\phantom{9999}\\\underline{\phantom{\times}45\phantom{99999}}\\\phantom{\times}4888455\end{array}
Now add the intermediate results to get final answer.