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\begin{array}{c}\phantom{\times999}2627\\\underline{\times\phantom{999}1572}\\\end{array}
First line up the numbers vertically and match the places from the right like this.
\begin{array}{c}\phantom{\times999}2627\\\underline{\times\phantom{999}1572}\\\phantom{\times999}5254\\\end{array}
Now multiply the first number with the 1^{st} digit in 2^{nd} number to get intermediate results. That is Multiply 2627 with 2. Write the result 5254 at the end leaving 0 spaces to the right like this.
\begin{array}{c}\phantom{\times999}2627\\\underline{\times\phantom{999}1572}\\\phantom{\times999}5254\\\phantom{\times9}18389\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 2627 with 7. Write the result 18389 at the end leaving 1 spaces to the right like this.
\begin{array}{c}\phantom{\times999}2627\\\underline{\times\phantom{999}1572}\\\phantom{\times999}5254\\\phantom{\times9}18389\phantom{9}\\\phantom{\times}13135\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 2627 with 5. Write the result 13135 at the end leaving 2 spaces to the right like this.
\begin{array}{c}\phantom{\times999}2627\\\underline{\times\phantom{999}1572}\\\phantom{\times999}5254\\\phantom{\times9}18389\phantom{9}\\\phantom{\times}13135\phantom{99}\\\underline{\phantom{\times}2627\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 2627 with 1. Write the result 2627 at the end leaving 3 spaces to the right like this.
\begin{array}{c}\phantom{\times999}2627\\\underline{\times\phantom{999}1572}\\\phantom{\times999}5254\\\phantom{\times9}18389\phantom{9}\\\phantom{\times}13135\phantom{99}\\\underline{\phantom{\times}2627\phantom{999}}\\\phantom{\times}4129644\end{array}
Now add the intermediate results to get final answer.