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\begin{array}{c}\phantom{\times99}3698552\\\underline{\times\phantom{99}2365599}\\\end{array}
First line up the numbers vertically and match the places from the right like this.
\begin{array}{c}\phantom{\times99}3698552\\\underline{\times\phantom{99}2365599}\\\phantom{\times9}33286968\\\end{array}
Now multiply the first number with the 1^{st} digit in 2^{nd} number to get intermediate results. That is Multiply 3698552 with 9. Write the result 33286968 at the end leaving 0 spaces to the right like this.
\begin{array}{c}\phantom{\times99}3698552\\\underline{\times\phantom{99}2365599}\\\phantom{\times9}33286968\\\phantom{\times}33286968\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 3698552 with 9. Write the result 33286968 at the end leaving 1 spaces to the right like this.
\begin{array}{c}\phantom{\times99}3698552\\\underline{\times\phantom{99}2365599}\\\phantom{\times9}33286968\\\phantom{\times}33286968\phantom{9}\\\phantom{\times}18492760\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 3698552 with 5. Write the result 18492760 at the end leaving 2 spaces to the right like this.
\begin{array}{c}\phantom{\times99}3698552\\\underline{\times\phantom{99}2365599}\\\phantom{\times9}33286968\\\phantom{\times}33286968\phantom{9}\\\phantom{\times}18492760\phantom{99}\\\phantom{\times}18492760\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 3698552 with 5. Write the result 18492760 at the end leaving 3 spaces to the right like this.
\begin{array}{c}\phantom{\times99}3698552\\\underline{\times\phantom{99}2365599}\\\phantom{\times9}33286968\\\phantom{\times}33286968\phantom{9}\\\phantom{\times}18492760\phantom{99}\\\phantom{\times}18492760\phantom{999}\\\phantom{\times}22191312\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 3698552 with 6. Write the result 22191312 at the end leaving 4 spaces to the right like this.
\begin{array}{c}\phantom{\times99}3698552\\\underline{\times\phantom{99}2365599}\\\phantom{\times9}33286968\\\phantom{\times}33286968\phantom{9}\\\phantom{\times}18492760\phantom{99}\\\phantom{\times}18492760\phantom{999}\\\phantom{\times}22191312\phantom{9999}\\\phantom{\times}11095656\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 3698552 with 3. Write the result 11095656 at the end leaving 5 spaces to the right like this.
\begin{array}{c}\phantom{\times99}3698552\\\underline{\times\phantom{99}2365599}\\\phantom{\times9}33286968\\\phantom{\times}33286968\phantom{9}\\\phantom{\times}18492760\phantom{99}\\\phantom{\times}18492760\phantom{999}\\\phantom{\times}22191312\phantom{9999}\\\phantom{\times}11095656\phantom{99999}\\\underline{\phantom{\times}7397104\phantom{999999}}\\\end{array}
Now multiply the first number with the 7^{th} digit in 2^{nd} number to get intermediate results. That is Multiply 3698552 with 2. Write the result 7397104 at the end leaving 6 spaces to the right like this.
\begin{array}{c}\phantom{\times99}3698552\\\underline{\times\phantom{99}2365599}\\\phantom{\times9}33286968\\\phantom{\times}33286968\phantom{9}\\\phantom{\times}18492760\phantom{99}\\\phantom{\times}18492760\phantom{999}\\\phantom{\times}22191312\phantom{9999}\\\phantom{\times}11095656\phantom{99999}\\\underline{\phantom{\times}7397104\phantom{999999}}\\\phantom{\times}442530696\end{array}
Now add the intermediate results to get final answer.