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\begin{array}{c}\phantom{\times999999}699\\\underline{\times\phantom{999}533788}\\\end{array}
First line up the numbers vertically and match the places from the right like this.
\begin{array}{c}\phantom{\times999999}699\\\underline{\times\phantom{999}533788}\\\phantom{\times99999}5592\\\end{array}
Now multiply the first number with the 1^{st} digit in 2^{nd} number to get intermediate results. That is Multiply 699 with 8. Write the result 5592 at the end leaving 0 spaces to the right like this.
\begin{array}{c}\phantom{\times999999}699\\\underline{\times\phantom{999}533788}\\\phantom{\times99999}5592\\\phantom{\times9999}5592\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 699 with 8. Write the result 5592 at the end leaving 1 spaces to the right like this.
\begin{array}{c}\phantom{\times999999}699\\\underline{\times\phantom{999}533788}\\\phantom{\times99999}5592\\\phantom{\times9999}5592\phantom{9}\\\phantom{\times999}4893\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 699 with 7. Write the result 4893 at the end leaving 2 spaces to the right like this.
\begin{array}{c}\phantom{\times999999}699\\\underline{\times\phantom{999}533788}\\\phantom{\times99999}5592\\\phantom{\times9999}5592\phantom{9}\\\phantom{\times999}4893\phantom{99}\\\phantom{\times99}2097\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 699 with 3. Write the result 2097 at the end leaving 3 spaces to the right like this.
\begin{array}{c}\phantom{\times999999}699\\\underline{\times\phantom{999}533788}\\\phantom{\times99999}5592\\\phantom{\times9999}5592\phantom{9}\\\phantom{\times999}4893\phantom{99}\\\phantom{\times99}2097\phantom{999}\\\phantom{\times9}2097\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 699 with 3. Write the result 2097 at the end leaving 4 spaces to the right like this.
\begin{array}{c}\phantom{\times999999}699\\\underline{\times\phantom{999}533788}\\\phantom{\times99999}5592\\\phantom{\times9999}5592\phantom{9}\\\phantom{\times999}4893\phantom{99}\\\phantom{\times99}2097\phantom{999}\\\phantom{\times9}2097\phantom{9999}\\\underline{\phantom{\times}3495\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 699 with 5. Write the result 3495 at the end leaving 5 spaces to the right like this.
\begin{array}{c}\phantom{\times999999}699\\\underline{\times\phantom{999}533788}\\\phantom{\times99999}5592\\\phantom{\times9999}5592\phantom{9}\\\phantom{\times999}4893\phantom{99}\\\phantom{\times99}2097\phantom{999}\\\phantom{\times9}2097\phantom{9999}\\\underline{\phantom{\times}3495\phantom{99999}}\\\phantom{\times}373117812\end{array}
Now add the intermediate results to get final answer.