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\begin{array}{c}\phantom{\times9999}771736\\\underline{\times\phantom{999999}1736}\\\end{array}
First line up the numbers vertically and match the places from the right like this.
\begin{array}{c}\phantom{\times9999}771736\\\underline{\times\phantom{999999}1736}\\\phantom{\times999}4630416\\\end{array}
Now multiply the first number with the 1^{st} digit in 2^{nd} number to get intermediate results. That is Multiply 771736 with 6. Write the result 4630416 at the end leaving 0 spaces to the right like this.
\begin{array}{c}\phantom{\times9999}771736\\\underline{\times\phantom{999999}1736}\\\phantom{\times999}4630416\\\phantom{\times99}2315208\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 771736 with 3. Write the result 2315208 at the end leaving 1 spaces to the right like this.
\begin{array}{c}\phantom{\times9999}771736\\\underline{\times\phantom{999999}1736}\\\phantom{\times999}4630416\\\phantom{\times99}2315208\phantom{9}\\\phantom{\times9}5402152\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 771736 with 7. Write the result 5402152 at the end leaving 2 spaces to the right like this.
\begin{array}{c}\phantom{\times9999}771736\\\underline{\times\phantom{999999}1736}\\\phantom{\times999}4630416\\\phantom{\times99}2315208\phantom{9}\\\phantom{\times9}5402152\phantom{99}\\\underline{\phantom{\times9}771736\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 771736 with 1. Write the result 771736 at the end leaving 3 spaces to the right like this.
\begin{array}{c}\phantom{\times9999}771736\\\underline{\times\phantom{999999}1736}\\\phantom{\times999}4630416\\\phantom{\times99}2315208\phantom{9}\\\phantom{\times9}5402152\phantom{99}\\\underline{\phantom{\times9}771736\phantom{999}}\\\phantom{\times}1339733696\end{array}
Now add the intermediate results to get final answer.