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\begin{array}{c}\phantom{\times999999}776\\\underline{\times\phantom{9}33491271}\\\end{array}
First line up the numbers vertically and match the places from the right like this.
\begin{array}{c}\phantom{\times999999}776\\\underline{\times\phantom{9}33491271}\\\phantom{\times999999}776\\\end{array}
Now multiply the first number with the 1^{st} digit in 2^{nd} number to get intermediate results. That is Multiply 776 with 1. Write the result 776 at the end leaving 0 spaces to the right like this.
\begin{array}{c}\phantom{\times999999}776\\\underline{\times\phantom{9}33491271}\\\phantom{\times999999}776\\\phantom{\times9999}5432\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 776 with 7. Write the result 5432 at the end leaving 1 spaces to the right like this.
\begin{array}{c}\phantom{\times999999}776\\\underline{\times\phantom{9}33491271}\\\phantom{\times999999}776\\\phantom{\times9999}5432\phantom{9}\\\phantom{\times999}1552\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 776 with 2. Write the result 1552 at the end leaving 2 spaces to the right like this.
\begin{array}{c}\phantom{\times999999}776\\\underline{\times\phantom{9}33491271}\\\phantom{\times999999}776\\\phantom{\times9999}5432\phantom{9}\\\phantom{\times999}1552\phantom{99}\\\phantom{\times999}776\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 776 with 1. Write the result 776 at the end leaving 3 spaces to the right like this.
\begin{array}{c}\phantom{\times999999}776\\\underline{\times\phantom{9}33491271}\\\phantom{\times999999}776\\\phantom{\times9999}5432\phantom{9}\\\phantom{\times999}1552\phantom{99}\\\phantom{\times999}776\phantom{999}\\\phantom{\times9}6984\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 776 with 9. Write the result 6984 at the end leaving 4 spaces to the right like this.
\begin{array}{c}\phantom{\times999999}776\\\underline{\times\phantom{9}33491271}\\\phantom{\times999999}776\\\phantom{\times9999}5432\phantom{9}\\\phantom{\times999}1552\phantom{99}\\\phantom{\times999}776\phantom{999}\\\phantom{\times9}6984\phantom{9999}\\\phantom{\times}3104\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 776 with 4. Write the result 3104 at the end leaving 5 spaces to the right like this.
\begin{array}{c}\phantom{\times999999}776\\\underline{\times\phantom{9}33491271}\\\phantom{\times999999}776\\\phantom{\times9999}5432\phantom{9}\\\phantom{\times999}1552\phantom{99}\\\phantom{\times999}776\phantom{999}\\\phantom{\times9}6984\phantom{9999}\\\phantom{\times}3104\phantom{99999}\\\phantom{\times}2328\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 776 with 3. Write the result 2328 at the end leaving 6 spaces to the right like this.
\begin{array}{c}\phantom{\times999999}776\\\underline{\times\phantom{9}33491271}\\\phantom{\times999999}776\\\phantom{\times9999}5432\phantom{9}\\\phantom{\times999}1552\phantom{99}\\\phantom{\times999}776\phantom{999}\\\phantom{\times9}6984\phantom{9999}\\\phantom{\times}3104\phantom{99999}\\\phantom{\times}2328\phantom{999999}\\\underline{\phantom{\times}2328\phantom{9999999}}\\\end{array}
Now multiply the first number with the 8^{th} digit in 2^{nd} number to get intermediate results. That is Multiply 776 with 3. Write the result 2328 at the end leaving 7 spaces to the right like this.
\begin{array}{c}\phantom{\times999999}776\\\underline{\times\phantom{9}33491271}\\\phantom{\times999999}776\\\phantom{\times9999}5432\phantom{9}\\\phantom{\times999}1552\phantom{99}\\\phantom{\times999}776\phantom{999}\\\phantom{\times9}6984\phantom{9999}\\\phantom{\times}3104\phantom{99999}\\\phantom{\times}2328\phantom{999999}\\\underline{\phantom{\times}2328\phantom{9999999}}\\\phantom{\times}219422520\end{array}
Now add the intermediate results to get final answer.