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\begin{array}{c}\phantom{\times999}6280\\\underline{\times\phantom{999}1256}\\\end{array}
First line up the numbers vertically and match the places from the right like this.
\begin{array}{c}\phantom{\times999}6280\\\underline{\times\phantom{999}1256}\\\phantom{\times99}37680\\\end{array}
Now multiply the first number with the 1^{st} digit in 2^{nd} number to get intermediate results. That is Multiply 6280 with 6. Write the result 37680 at the end leaving 0 spaces to the right like this.
\begin{array}{c}\phantom{\times999}6280\\\underline{\times\phantom{999}1256}\\\phantom{\times99}37680\\\phantom{\times9}31400\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 6280 with 5. Write the result 31400 at the end leaving 1 spaces to the right like this.
\begin{array}{c}\phantom{\times999}6280\\\underline{\times\phantom{999}1256}\\\phantom{\times99}37680\\\phantom{\times9}31400\phantom{9}\\\phantom{\times}12560\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 6280 with 2. Write the result 12560 at the end leaving 2 spaces to the right like this.
\begin{array}{c}\phantom{\times999}6280\\\underline{\times\phantom{999}1256}\\\phantom{\times99}37680\\\phantom{\times9}31400\phantom{9}\\\phantom{\times}12560\phantom{99}\\\underline{\phantom{\times}6280\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 6280 with 1. Write the result 6280 at the end leaving 3 spaces to the right like this.
\begin{array}{c}\phantom{\times999}6280\\\underline{\times\phantom{999}1256}\\\phantom{\times99}37680\\\phantom{\times9}31400\phantom{9}\\\phantom{\times}12560\phantom{99}\\\underline{\phantom{\times}6280\phantom{999}}\\\phantom{\times}7887680\end{array}
Now add the intermediate results to get final answer.