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\begin{array}{c}\phantom{\times999}123421\\\underline{\times\phantom{999}666666}\\\end{array}
First line up the numbers vertically and match the places from the right like this.
\begin{array}{c}\phantom{\times999}123421\\\underline{\times\phantom{999}666666}\\\phantom{\times999}740526\\\end{array}
Now multiply the first number with the 1^{st} digit in 2^{nd} number to get intermediate results. That is Multiply 123421 with 6. Write the result 740526 at the end leaving 0 spaces to the right like this.
\begin{array}{c}\phantom{\times999}123421\\\underline{\times\phantom{999}666666}\\\phantom{\times999}740526\\\phantom{\times99}740526\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 123421 with 6. Write the result 740526 at the end leaving 1 spaces to the right like this.
\begin{array}{c}\phantom{\times999}123421\\\underline{\times\phantom{999}666666}\\\phantom{\times999}740526\\\phantom{\times99}740526\phantom{9}\\\phantom{\times9}740526\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 123421 with 6. Write the result 740526 at the end leaving 2 spaces to the right like this.
\begin{array}{c}\phantom{\times999}123421\\\underline{\times\phantom{999}666666}\\\phantom{\times999}740526\\\phantom{\times99}740526\phantom{9}\\\phantom{\times9}740526\phantom{99}\\\phantom{\times}740526\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 123421 with 6. Write the result 740526 at the end leaving 3 spaces to the right like this.
\begin{array}{c}\phantom{\times999}123421\\\underline{\times\phantom{999}666666}\\\phantom{\times999}740526\\\phantom{\times99}740526\phantom{9}\\\phantom{\times9}740526\phantom{99}\\\phantom{\times}740526\phantom{999}\\\phantom{\times}740526\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 123421 with 6. Write the result 740526 at the end leaving 4 spaces to the right like this.
\begin{array}{c}\phantom{\times999}123421\\\underline{\times\phantom{999}666666}\\\phantom{\times999}740526\\\phantom{\times99}740526\phantom{9}\\\phantom{\times9}740526\phantom{99}\\\phantom{\times}740526\phantom{999}\\\phantom{\times}740526\phantom{9999}\\\underline{\phantom{\times}740526\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 123421 with 6. Write the result 740526 at the end leaving 5 spaces to the right like this.
\begin{array}{c}\phantom{\times999}123421\\\underline{\times\phantom{999}666666}\\\phantom{\times999}740526\\\phantom{\times99}740526\phantom{9}\\\phantom{\times9}740526\phantom{99}\\\phantom{\times}740526\phantom{999}\\\phantom{\times}740526\phantom{9999}\\\underline{\phantom{\times}740526\phantom{99999}}\\\phantom{\times}676205762\end{array}
Now add the intermediate results to get final answer.