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\begin{array}{c}\phantom{\times}42455288\\\underline{\times\phantom{}5553}\\\end{array}
First line up the numbers vertically and match the places from the right like this.
\begin{array}{c}\phantom{\times}42455288\\\underline{\times\phantom{}5553}\\\phantom{\times}127365864\\\end{array}
Now multiply the first number with the 1^{st} digit in 2^{nd} number to get intermediate results. That is Multiply 42455288 with 3. Write the result 127365864 at the end leaving 0 spaces to the right like this.
\begin{array}{c}\phantom{\times}42455288\\\underline{\times\phantom{}5553}\\\phantom{\times}127365864\\\phantom{\times}212276440\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 42455288 with 5. Write the result 212276440 at the end leaving 1 spaces to the right like this.
\begin{array}{c}\phantom{\times}42455288\\\underline{\times\phantom{}5553}\\\phantom{\times}127365864\\\phantom{\times}212276440\phantom{9}\\\phantom{\times}212276440\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 42455288 with 5. Write the result 212276440 at the end leaving 2 spaces to the right like this.
\begin{array}{c}\phantom{\times}42455288\\\underline{\times\phantom{}5553}\\\phantom{\times}127365864\\\phantom{\times}212276440\phantom{9}\\\phantom{\times}212276440\phantom{99}\\\underline{\phantom{\times}212276440\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 42455288 with 5. Write the result 212276440 at the end leaving 3 spaces to the right like this.
\begin{array}{c}\phantom{\times}42455288\\\underline{\times\phantom{}5553}\\\phantom{\times}127365864\\\phantom{\times}212276440\phantom{9}\\\phantom{\times}212276440\phantom{99}\\\underline{\phantom{\times}212276440\phantom{999}}\\\phantom{\times}-468987016\end{array}
Now add the intermediate results to get final answer.