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\begin{array}{c}\phantom{\times9999}76389\\\underline{\times\phantom{99999}7253}\\\end{array}
First line up the numbers vertically and match the places from the right like this.
\begin{array}{c}\phantom{\times9999}76389\\\underline{\times\phantom{99999}7253}\\\phantom{\times999}229167\\\end{array}
Now multiply the first number with the 1^{st} digit in 2^{nd} number to get intermediate results. That is Multiply 76389 with 3. Write the result 229167 at the end leaving 0 spaces to the right like this.
\begin{array}{c}\phantom{\times9999}76389\\\underline{\times\phantom{99999}7253}\\\phantom{\times999}229167\\\phantom{\times99}381945\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 76389 with 5. Write the result 381945 at the end leaving 1 spaces to the right like this.
\begin{array}{c}\phantom{\times9999}76389\\\underline{\times\phantom{99999}7253}\\\phantom{\times999}229167\\\phantom{\times99}381945\phantom{9}\\\phantom{\times9}152778\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 76389 with 2. Write the result 152778 at the end leaving 2 spaces to the right like this.
\begin{array}{c}\phantom{\times9999}76389\\\underline{\times\phantom{99999}7253}\\\phantom{\times999}229167\\\phantom{\times99}381945\phantom{9}\\\phantom{\times9}152778\phantom{99}\\\underline{\phantom{\times}534723\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 76389 with 7. Write the result 534723 at the end leaving 3 spaces to the right like this.
\begin{array}{c}\phantom{\times9999}76389\\\underline{\times\phantom{99999}7253}\\\phantom{\times999}229167\\\phantom{\times99}381945\phantom{9}\\\phantom{\times9}152778\phantom{99}\\\underline{\phantom{\times}534723\phantom{999}}\\\phantom{\times}554049417\end{array}
Now add the intermediate results to get final answer.