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\begin{array}{c}\phantom{\times9999}7654\\\underline{\times\phantom{999}12345}\\\end{array}
First line up the numbers vertically and match the places from the right like this.
\begin{array}{c}\phantom{\times9999}7654\\\underline{\times\phantom{999}12345}\\\phantom{\times999}38270\\\end{array}
Now multiply the first number with the 1^{st} digit in 2^{nd} number to get intermediate results. That is Multiply 7654 with 5. Write the result 38270 at the end leaving 0 spaces to the right like this.
\begin{array}{c}\phantom{\times9999}7654\\\underline{\times\phantom{999}12345}\\\phantom{\times999}38270\\\phantom{\times99}30616\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 7654 with 4. Write the result 30616 at the end leaving 1 spaces to the right like this.
\begin{array}{c}\phantom{\times9999}7654\\\underline{\times\phantom{999}12345}\\\phantom{\times999}38270\\\phantom{\times99}30616\phantom{9}\\\phantom{\times9}22962\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 7654 with 3. Write the result 22962 at the end leaving 2 spaces to the right like this.
\begin{array}{c}\phantom{\times9999}7654\\\underline{\times\phantom{999}12345}\\\phantom{\times999}38270\\\phantom{\times99}30616\phantom{9}\\\phantom{\times9}22962\phantom{99}\\\phantom{\times}15308\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 7654 with 2. Write the result 15308 at the end leaving 3 spaces to the right like this.
\begin{array}{c}\phantom{\times9999}7654\\\underline{\times\phantom{999}12345}\\\phantom{\times999}38270\\\phantom{\times99}30616\phantom{9}\\\phantom{\times9}22962\phantom{99}\\\phantom{\times}15308\phantom{999}\\\underline{\phantom{\times}7654\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 7654 with 1. Write the result 7654 at the end leaving 4 spaces to the right like this.
\begin{array}{c}\phantom{\times9999}7654\\\underline{\times\phantom{999}12345}\\\phantom{\times999}38270\\\phantom{\times99}30616\phantom{9}\\\phantom{\times9}22962\phantom{99}\\\phantom{\times}15308\phantom{999}\\\underline{\phantom{\times}7654\phantom{9999}}\\\phantom{\times}94488630\end{array}
Now add the intermediate results to get final answer.