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\begin{array}{c}\phantom{\times}200252\\\underline{\times\phantom{}253887}\\\end{array}
First line up the numbers vertically and match the places from the right like this.
\begin{array}{c}\phantom{\times}200252\\\underline{\times\phantom{}253887}\\\phantom{\times}1401764\\\end{array}
Now multiply the first number with the 1^{st} digit in 2^{nd} number to get intermediate results. That is Multiply 200252 with 7. Write the result 1401764 at the end leaving 0 spaces to the right like this.
\begin{array}{c}\phantom{\times}200252\\\underline{\times\phantom{}253887}\\\phantom{\times}1401764\\\phantom{\times}1602016\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 200252 with 8. Write the result 1602016 at the end leaving 1 spaces to the right like this.
\begin{array}{c}\phantom{\times}200252\\\underline{\times\phantom{}253887}\\\phantom{\times}1401764\\\phantom{\times}1602016\phantom{9}\\\phantom{\times}1602016\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 200252 with 8. Write the result 1602016 at the end leaving 2 spaces to the right like this.
\begin{array}{c}\phantom{\times}200252\\\underline{\times\phantom{}253887}\\\phantom{\times}1401764\\\phantom{\times}1602016\phantom{9}\\\phantom{\times}1602016\phantom{99}\\\phantom{\times}600756\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 200252 with 3. Write the result 600756 at the end leaving 3 spaces to the right like this.
\begin{array}{c}\phantom{\times}200252\\\underline{\times\phantom{}253887}\\\phantom{\times}1401764\\\phantom{\times}1602016\phantom{9}\\\phantom{\times}1602016\phantom{99}\\\phantom{\times}600756\phantom{999}\\\phantom{\times}1001260\phantom{9999}\\\end{array}
Now multiply the first number with the 5^{th} digit in 2^{nd} number to get intermediate results. That is Multiply 200252 with 5. Write the result 1001260 at the end leaving 4 spaces to the right like this.
\begin{array}{c}\phantom{\times}200252\\\underline{\times\phantom{}253887}\\\phantom{\times}1401764\\\phantom{\times}1602016\phantom{9}\\\phantom{\times}1602016\phantom{99}\\\phantom{\times}600756\phantom{999}\\\phantom{\times}1001260\phantom{9999}\\\underline{\phantom{\times}400504\phantom{99999}}\\\end{array}
Now multiply the first number with the 6^{th} digit in 2^{nd} number to get intermediate results. That is Multiply 200252 with 2. Write the result 400504 at the end leaving 5 spaces to the right like this.
\begin{array}{c}\phantom{\times}200252\\\underline{\times\phantom{}253887}\\\phantom{\times}1401764\\\phantom{\times}1602016\phantom{9}\\\phantom{\times}1602016\phantom{99}\\\phantom{\times}600756\phantom{999}\\\phantom{\times}1001260\phantom{9999}\\\underline{\phantom{\times}400504\phantom{99999}}\\\phantom{\times}-698228028\end{array}
Now add the intermediate results to get final answer.