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\begin{array}{c}\phantom{\times}95223142\\\underline{\times\phantom{}65429}\\\end{array}
First line up the numbers vertically and match the places from the right like this.
\begin{array}{c}\phantom{\times}95223142\\\underline{\times\phantom{}65429}\\\phantom{\times}857008278\\\end{array}
Now multiply the first number with the 1^{st} digit in 2^{nd} number to get intermediate results. That is Multiply 95223142 with 9. Write the result 857008278 at the end leaving 0 spaces to the right like this.
\begin{array}{c}\phantom{\times}95223142\\\underline{\times\phantom{}65429}\\\phantom{\times}857008278\\\phantom{\times}190446284\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 95223142 with 2. Write the result 190446284 at the end leaving 1 spaces to the right like this.
\begin{array}{c}\phantom{\times}95223142\\\underline{\times\phantom{}65429}\\\phantom{\times}857008278\\\phantom{\times}190446284\phantom{9}\\\phantom{\times}380892568\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 95223142 with 4. Write the result 380892568 at the end leaving 2 spaces to the right like this.
\begin{array}{c}\phantom{\times}95223142\\\underline{\times\phantom{}65429}\\\phantom{\times}857008278\\\phantom{\times}190446284\phantom{9}\\\phantom{\times}380892568\phantom{99}\\\phantom{\times}476115710\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 95223142 with 5. Write the result 476115710 at the end leaving 3 spaces to the right like this.
\begin{array}{c}\phantom{\times}95223142\\\underline{\times\phantom{}65429}\\\phantom{\times}857008278\\\phantom{\times}190446284\phantom{9}\\\phantom{\times}380892568\phantom{99}\\\phantom{\times}476115710\phantom{999}\\\underline{\phantom{\times}571338852\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 95223142 with 6. Write the result 571338852 at the end leaving 4 spaces to the right like this.
\begin{array}{c}\phantom{\times}95223142\\\underline{\times\phantom{}65429}\\\phantom{\times}857008278\\\phantom{\times}190446284\phantom{9}\\\phantom{\times}380892568\phantom{99}\\\phantom{\times}476115710\phantom{999}\\\underline{\phantom{\times}571338852\phantom{9999}}\\\phantom{\times}-1642588578\end{array}
Now add the intermediate results to get final answer.