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\begin{array}{c}\phantom{\times999}7413100\\\underline{\times\phantom{9999}359996}\\\end{array}
First line up the numbers vertically and match the places from the right like this.
\begin{array}{c}\phantom{\times999}7413100\\\underline{\times\phantom{9999}359996}\\\phantom{\times99}44478600\\\end{array}
Now multiply the first number with the 1^{st} digit in 2^{nd} number to get intermediate results. That is Multiply 7413100 with 6. Write the result 44478600 at the end leaving 0 spaces to the right like this.
\begin{array}{c}\phantom{\times999}7413100\\\underline{\times\phantom{9999}359996}\\\phantom{\times99}44478600\\\phantom{\times9}66717900\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 7413100 with 9. Write the result 66717900 at the end leaving 1 spaces to the right like this.
\begin{array}{c}\phantom{\times999}7413100\\\underline{\times\phantom{9999}359996}\\\phantom{\times99}44478600\\\phantom{\times9}66717900\phantom{9}\\\phantom{\times}66717900\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 7413100 with 9. Write the result 66717900 at the end leaving 2 spaces to the right like this.
\begin{array}{c}\phantom{\times999}7413100\\\underline{\times\phantom{9999}359996}\\\phantom{\times99}44478600\\\phantom{\times9}66717900\phantom{9}\\\phantom{\times}66717900\phantom{99}\\\phantom{\times}66717900\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 7413100 with 9. Write the result 66717900 at the end leaving 3 spaces to the right like this.
\begin{array}{c}\phantom{\times999}7413100\\\underline{\times\phantom{9999}359996}\\\phantom{\times99}44478600\\\phantom{\times9}66717900\phantom{9}\\\phantom{\times}66717900\phantom{99}\\\phantom{\times}66717900\phantom{999}\\\phantom{\times}37065500\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 7413100 with 5. Write the result 37065500 at the end leaving 4 spaces to the right like this.
\begin{array}{c}\phantom{\times999}7413100\\\underline{\times\phantom{9999}359996}\\\phantom{\times99}44478600\\\phantom{\times9}66717900\phantom{9}\\\phantom{\times}66717900\phantom{99}\\\phantom{\times}66717900\phantom{999}\\\phantom{\times}37065500\phantom{9999}\\\underline{\phantom{\times}22239300\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 7413100 with 3. Write the result 22239300 at the end leaving 5 spaces to the right like this.
\begin{array}{c}\phantom{\times999}7413100\\\underline{\times\phantom{9999}359996}\\\phantom{\times99}44478600\\\phantom{\times9}66717900\phantom{9}\\\phantom{\times}66717900\phantom{99}\\\phantom{\times}66717900\phantom{999}\\\phantom{\times}37065500\phantom{9999}\\\underline{\phantom{\times}22239300\phantom{99999}}\\\phantom{\times}1511656784\end{array}
Now add the intermediate results to get final answer.