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\begin{array}{c}\phantom{\times999}99\\\underline{\times\phantom{99}774}\\\end{array}
First line up the numbers vertically and match the places from the right like this.
\begin{array}{c}\phantom{\times999}99\\\underline{\times\phantom{99}774}\\\phantom{\times99}396\\\end{array}
Now multiply the first number with the 1^{st} digit in 2^{nd} number to get intermediate results. That is Multiply 99 with 4. Write the result 396 at the end leaving 0 spaces to the right like this.
\begin{array}{c}\phantom{\times999}99\\\underline{\times\phantom{99}774}\\\phantom{\times99}396\\\phantom{\times9}693\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 99 with 7. Write the result 693 at the end leaving 1 spaces to the right like this.
\begin{array}{c}\phantom{\times999}99\\\underline{\times\phantom{99}774}\\\phantom{\times99}396\\\phantom{\times9}693\phantom{9}\\\underline{\phantom{\times}693\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 99 with 7. Write the result 693 at the end leaving 2 spaces to the right like this.
\begin{array}{c}\phantom{\times999}99\\\underline{\times\phantom{99}774}\\\phantom{\times99}396\\\phantom{\times9}693\phantom{9}\\\underline{\phantom{\times}693\phantom{99}}\\\phantom{\times}76626\end{array}
Now add the intermediate results to get final answer.