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\begin{array}{c}\phantom{\times}77\\\underline{\times\phantom{}90259341}\\\end{array}
First line up the numbers vertically and match the places from the right like this.
\begin{array}{c}\phantom{\times}77\\\underline{\times\phantom{}90259341}\\\phantom{\times}77\\\end{array}
Now multiply the first number with the 1^{st} digit in 2^{nd} number to get intermediate results. That is Multiply 77 with 1. Write the result 77 at the end leaving 0 spaces to the right like this.
\begin{array}{c}\phantom{\times}77\\\underline{\times\phantom{}90259341}\\\phantom{\times}77\\\phantom{\times}308\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 77 with 4. Write the result 308 at the end leaving 1 spaces to the right like this.
\begin{array}{c}\phantom{\times}77\\\underline{\times\phantom{}90259341}\\\phantom{\times}77\\\phantom{\times}308\phantom{9}\\\phantom{\times}231\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 77 with 3. Write the result 231 at the end leaving 2 spaces to the right like this.
\begin{array}{c}\phantom{\times}77\\\underline{\times\phantom{}90259341}\\\phantom{\times}77\\\phantom{\times}308\phantom{9}\\\phantom{\times}231\phantom{99}\\\phantom{\times}693\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 77 with 9. Write the result 693 at the end leaving 3 spaces to the right like this.
\begin{array}{c}\phantom{\times}77\\\underline{\times\phantom{}90259341}\\\phantom{\times}77\\\phantom{\times}308\phantom{9}\\\phantom{\times}231\phantom{99}\\\phantom{\times}693\phantom{999}\\\phantom{\times}385\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 77 with 5. Write the result 385 at the end leaving 4 spaces to the right like this.
\begin{array}{c}\phantom{\times}77\\\underline{\times\phantom{}90259341}\\\phantom{\times}77\\\phantom{\times}308\phantom{9}\\\phantom{\times}231\phantom{99}\\\phantom{\times}693\phantom{999}\\\phantom{\times}385\phantom{9999}\\\phantom{\times}154\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 77 with 2. Write the result 154 at the end leaving 5 spaces to the right like this.
\begin{array}{c}\phantom{\times}77\\\underline{\times\phantom{}90259341}\\\phantom{\times}77\\\phantom{\times}308\phantom{9}\\\phantom{\times}231\phantom{99}\\\phantom{\times}693\phantom{999}\\\phantom{\times}385\phantom{9999}\\\phantom{\times}154\phantom{99999}\\\phantom{\times}0\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 77 with 0. Write the result 0 at the end leaving 6 spaces to the right like this.
\begin{array}{c}\phantom{\times}77\\\underline{\times\phantom{}90259341}\\\phantom{\times}77\\\phantom{\times}308\phantom{9}\\\phantom{\times}231\phantom{99}\\\phantom{\times}693\phantom{999}\\\phantom{\times}385\phantom{9999}\\\phantom{\times}154\phantom{99999}\\\phantom{\times}0\phantom{999999}\\\underline{\phantom{\times}693\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 77 with 9. Write the result 693 at the end leaving 7 spaces to the right like this.
\begin{array}{c}\phantom{\times}77\\\underline{\times\phantom{}90259341}\\\phantom{\times}77\\\phantom{\times}308\phantom{9}\\\phantom{\times}231\phantom{99}\\\phantom{\times}693\phantom{999}\\\phantom{\times}385\phantom{9999}\\\phantom{\times}154\phantom{99999}\\\phantom{\times}0\phantom{999999}\\\underline{\phantom{\times}693\phantom{9999999}}\\\phantom{\times}-1639965335\end{array}
Now add the intermediate results to get final answer.