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\begin{array}{c}\phantom{\times9999}956\\\underline{\times\phantom{999}6346}\\\end{array}
First line up the numbers vertically and match the places from the right like this.
\begin{array}{c}\phantom{\times9999}956\\\underline{\times\phantom{999}6346}\\\phantom{\times999}5736\\\end{array}
Now multiply the first number with the 1^{st} digit in 2^{nd} number to get intermediate results. That is Multiply 956 with 6. Write the result 5736 at the end leaving 0 spaces to the right like this.
\begin{array}{c}\phantom{\times9999}956\\\underline{\times\phantom{999}6346}\\\phantom{\times999}5736\\\phantom{\times99}3824\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 956 with 4. Write the result 3824 at the end leaving 1 spaces to the right like this.
\begin{array}{c}\phantom{\times9999}956\\\underline{\times\phantom{999}6346}\\\phantom{\times999}5736\\\phantom{\times99}3824\phantom{9}\\\phantom{\times9}2868\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 956 with 3. Write the result 2868 at the end leaving 2 spaces to the right like this.
\begin{array}{c}\phantom{\times9999}956\\\underline{\times\phantom{999}6346}\\\phantom{\times999}5736\\\phantom{\times99}3824\phantom{9}\\\phantom{\times9}2868\phantom{99}\\\underline{\phantom{\times}5736\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 956 with 6. Write the result 5736 at the end leaving 3 spaces to the right like this.
\begin{array}{c}\phantom{\times9999}956\\\underline{\times\phantom{999}6346}\\\phantom{\times999}5736\\\phantom{\times99}3824\phantom{9}\\\phantom{\times9}2868\phantom{99}\\\underline{\phantom{\times}5736\phantom{999}}\\\phantom{\times}6066776\end{array}
Now add the intermediate results to get final answer.