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\begin{array}{c}\phantom{\times999}2555556\\\underline{\times\phantom{999999}2465}\\\end{array}
First line up the numbers vertically and match the places from the right like this.
\begin{array}{c}\phantom{\times999}2555556\\\underline{\times\phantom{999999}2465}\\\phantom{\times99}12777780\\\end{array}
Now multiply the first number with the 1^{st} digit in 2^{nd} number to get intermediate results. That is Multiply 2555556 with 5. Write the result 12777780 at the end leaving 0 spaces to the right like this.
\begin{array}{c}\phantom{\times999}2555556\\\underline{\times\phantom{999999}2465}\\\phantom{\times99}12777780\\\phantom{\times9}15333336\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 2555556 with 6. Write the result 15333336 at the end leaving 1 spaces to the right like this.
\begin{array}{c}\phantom{\times999}2555556\\\underline{\times\phantom{999999}2465}\\\phantom{\times99}12777780\\\phantom{\times9}15333336\phantom{9}\\\phantom{\times}10222224\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 2555556 with 4. Write the result 10222224 at the end leaving 2 spaces to the right like this.
\begin{array}{c}\phantom{\times999}2555556\\\underline{\times\phantom{999999}2465}\\\phantom{\times99}12777780\\\phantom{\times9}15333336\phantom{9}\\\phantom{\times}10222224\phantom{99}\\\underline{\phantom{\times}5111112\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 2555556 with 2. Write the result 5111112 at the end leaving 3 spaces to the right like this.
\begin{array}{c}\phantom{\times999}2555556\\\underline{\times\phantom{999999}2465}\\\phantom{\times99}12777780\\\phantom{\times9}15333336\phantom{9}\\\phantom{\times}10222224\phantom{99}\\\underline{\phantom{\times}5111112\phantom{999}}\\\phantom{\times}2004478244\end{array}
Now add the intermediate results to get final answer.