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\begin{array}{c}\phantom{\times9999}969979\\\underline{\times\phantom{9999}979943}\\\end{array}
First line up the numbers vertically and match the places from the right like this.
\begin{array}{c}\phantom{\times9999}969979\\\underline{\times\phantom{9999}979943}\\\phantom{\times999}2909937\\\end{array}
Now multiply the first number with the 1^{st} digit in 2^{nd} number to get intermediate results. That is Multiply 969979 with 3. Write the result 2909937 at the end leaving 0 spaces to the right like this.
\begin{array}{c}\phantom{\times9999}969979\\\underline{\times\phantom{9999}979943}\\\phantom{\times999}2909937\\\phantom{\times99}3879916\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 969979 with 4. Write the result 3879916 at the end leaving 1 spaces to the right like this.
\begin{array}{c}\phantom{\times9999}969979\\\underline{\times\phantom{9999}979943}\\\phantom{\times999}2909937\\\phantom{\times99}3879916\phantom{9}\\\phantom{\times9}8729811\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 969979 with 9. Write the result 8729811 at the end leaving 2 spaces to the right like this.
\begin{array}{c}\phantom{\times9999}969979\\\underline{\times\phantom{9999}979943}\\\phantom{\times999}2909937\\\phantom{\times99}3879916\phantom{9}\\\phantom{\times9}8729811\phantom{99}\\\phantom{\times}8729811\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 969979 with 9. Write the result 8729811 at the end leaving 3 spaces to the right like this.
\begin{array}{c}\phantom{\times9999}969979\\\underline{\times\phantom{9999}979943}\\\phantom{\times999}2909937\\\phantom{\times99}3879916\phantom{9}\\\phantom{\times9}8729811\phantom{99}\\\phantom{\times}8729811\phantom{999}\\\phantom{\times}6789853\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 969979 with 7. Write the result 6789853 at the end leaving 4 spaces to the right like this.
\begin{array}{c}\phantom{\times9999}969979\\\underline{\times\phantom{9999}979943}\\\phantom{\times999}2909937\\\phantom{\times99}3879916\phantom{9}\\\phantom{\times9}8729811\phantom{99}\\\phantom{\times}8729811\phantom{999}\\\phantom{\times}6789853\phantom{9999}\\\underline{\phantom{\times}8729811\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 969979 with 9. Write the result 8729811 at the end leaving 5 spaces to the right like this.
\begin{array}{c}\phantom{\times9999}969979\\\underline{\times\phantom{9999}979943}\\\phantom{\times999}2909937\\\phantom{\times99}3879916\phantom{9}\\\phantom{\times9}8729811\phantom{99}\\\phantom{\times}8729811\phantom{999}\\\phantom{\times}6789853\phantom{9999}\\\underline{\phantom{\times}8729811\phantom{99999}}\\\phantom{\times}1336358781\end{array}
Now add the intermediate results to get final answer.