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\begin{array}{c}\phantom{\times}71755\\\underline{\times\phantom{}466642}\\\end{array}
First line up the numbers vertically and match the places from the right like this.
\begin{array}{c}\phantom{\times}71755\\\underline{\times\phantom{}466642}\\\phantom{\times}143510\\\end{array}
Now multiply the first number with the 1^{st} digit in 2^{nd} number to get intermediate results. That is Multiply 71755 with 2. Write the result 143510 at the end leaving 0 spaces to the right like this.
\begin{array}{c}\phantom{\times}71755\\\underline{\times\phantom{}466642}\\\phantom{\times}143510\\\phantom{\times}287020\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 71755 with 4. Write the result 287020 at the end leaving 1 spaces to the right like this.
\begin{array}{c}\phantom{\times}71755\\\underline{\times\phantom{}466642}\\\phantom{\times}143510\\\phantom{\times}287020\phantom{9}\\\phantom{\times}430530\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 71755 with 6. Write the result 430530 at the end leaving 2 spaces to the right like this.
\begin{array}{c}\phantom{\times}71755\\\underline{\times\phantom{}466642}\\\phantom{\times}143510\\\phantom{\times}287020\phantom{9}\\\phantom{\times}430530\phantom{99}\\\phantom{\times}430530\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 71755 with 6. Write the result 430530 at the end leaving 3 spaces to the right like this.
\begin{array}{c}\phantom{\times}71755\\\underline{\times\phantom{}466642}\\\phantom{\times}143510\\\phantom{\times}287020\phantom{9}\\\phantom{\times}430530\phantom{99}\\\phantom{\times}430530\phantom{999}\\\phantom{\times}430530\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 71755 with 6. Write the result 430530 at the end leaving 4 spaces to the right like this.
\begin{array}{c}\phantom{\times}71755\\\underline{\times\phantom{}466642}\\\phantom{\times}143510\\\phantom{\times}287020\phantom{9}\\\phantom{\times}430530\phantom{99}\\\phantom{\times}430530\phantom{999}\\\phantom{\times}430530\phantom{9999}\\\underline{\phantom{\times}287020\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 71755 with 4. Write the result 287020 at the end leaving 5 spaces to the right like this.
\begin{array}{c}\phantom{\times}71755\\\underline{\times\phantom{}466642}\\\phantom{\times}143510\\\phantom{\times}287020\phantom{9}\\\phantom{\times}430530\phantom{99}\\\phantom{\times}430530\phantom{999}\\\phantom{\times}430530\phantom{9999}\\\underline{\phantom{\times}287020\phantom{99999}}\\\phantom{\times}-875841658\end{array}
Now add the intermediate results to get final answer.