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\begin{array}{c}\phantom{\times9999}3428\\\underline{\times\phantom{9999}6359}\\\end{array}
First line up the numbers vertically and match the places from the right like this.
\begin{array}{c}\phantom{\times9999}3428\\\underline{\times\phantom{9999}6359}\\\phantom{\times999}30852\\\end{array}
Now multiply the first number with the 1^{st} digit in 2^{nd} number to get intermediate results. That is Multiply 3428 with 9. Write the result 30852 at the end leaving 0 spaces to the right like this.
\begin{array}{c}\phantom{\times9999}3428\\\underline{\times\phantom{9999}6359}\\\phantom{\times999}30852\\\phantom{\times99}17140\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 3428 with 5. Write the result 17140 at the end leaving 1 spaces to the right like this.
\begin{array}{c}\phantom{\times9999}3428\\\underline{\times\phantom{9999}6359}\\\phantom{\times999}30852\\\phantom{\times99}17140\phantom{9}\\\phantom{\times9}10284\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 3428 with 3. Write the result 10284 at the end leaving 2 spaces to the right like this.
\begin{array}{c}\phantom{\times9999}3428\\\underline{\times\phantom{9999}6359}\\\phantom{\times999}30852\\\phantom{\times99}17140\phantom{9}\\\phantom{\times9}10284\phantom{99}\\\underline{\phantom{\times}20568\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 3428 with 6. Write the result 20568 at the end leaving 3 spaces to the right like this.
\begin{array}{c}\phantom{\times9999}3428\\\underline{\times\phantom{9999}6359}\\\phantom{\times999}30852\\\phantom{\times99}17140\phantom{9}\\\phantom{\times9}10284\phantom{99}\\\underline{\phantom{\times}20568\phantom{999}}\\\phantom{\times}21798652\end{array}
Now add the intermediate results to get final answer.