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\begin{array}{c}\phantom{\times}34679\\\underline{\times\phantom{}98453}\\\end{array}
First line up the numbers vertically and match the places from the right like this.
\begin{array}{c}\phantom{\times}34679\\\underline{\times\phantom{}98453}\\\phantom{\times}104037\\\end{array}
Now multiply the first number with the 1^{st} digit in 2^{nd} number to get intermediate results. That is Multiply 34679 with 3. Write the result 104037 at the end leaving 0 spaces to the right like this.
\begin{array}{c}\phantom{\times}34679\\\underline{\times\phantom{}98453}\\\phantom{\times}104037\\\phantom{\times}173395\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 34679 with 5. Write the result 173395 at the end leaving 1 spaces to the right like this.
\begin{array}{c}\phantom{\times}34679\\\underline{\times\phantom{}98453}\\\phantom{\times}104037\\\phantom{\times}173395\phantom{9}\\\phantom{\times}138716\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 34679 with 4. Write the result 138716 at the end leaving 2 spaces to the right like this.
\begin{array}{c}\phantom{\times}34679\\\underline{\times\phantom{}98453}\\\phantom{\times}104037\\\phantom{\times}173395\phantom{9}\\\phantom{\times}138716\phantom{99}\\\phantom{\times}277432\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 34679 with 8. Write the result 277432 at the end leaving 3 spaces to the right like this.
\begin{array}{c}\phantom{\times}34679\\\underline{\times\phantom{}98453}\\\phantom{\times}104037\\\phantom{\times}173395\phantom{9}\\\phantom{\times}138716\phantom{99}\\\phantom{\times}277432\phantom{999}\\\underline{\phantom{\times}312111\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 34679 with 9. Write the result 312111 at the end leaving 4 spaces to the right like this.
\begin{array}{c}\phantom{\times}34679\\\underline{\times\phantom{}98453}\\\phantom{\times}104037\\\phantom{\times}173395\phantom{9}\\\phantom{\times}138716\phantom{99}\\\phantom{\times}277432\phantom{999}\\\underline{\phantom{\times}312111\phantom{9999}}\\\phantom{\times}-880715709\end{array}
Now add the intermediate results to get final answer.