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\begin{array}{c}\phantom{\times9999}29474\\\underline{\times\phantom{99999}3476}\\\end{array}
First line up the numbers vertically and match the places from the right like this.
\begin{array}{c}\phantom{\times9999}29474\\\underline{\times\phantom{99999}3476}\\\phantom{\times999}176844\\\end{array}
Now multiply the first number with the 1^{st} digit in 2^{nd} number to get intermediate results. That is Multiply 29474 with 6. Write the result 176844 at the end leaving 0 spaces to the right like this.
\begin{array}{c}\phantom{\times9999}29474\\\underline{\times\phantom{99999}3476}\\\phantom{\times999}176844\\\phantom{\times99}206318\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 29474 with 7. Write the result 206318 at the end leaving 1 spaces to the right like this.
\begin{array}{c}\phantom{\times9999}29474\\\underline{\times\phantom{99999}3476}\\\phantom{\times999}176844\\\phantom{\times99}206318\phantom{9}\\\phantom{\times9}117896\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 29474 with 4. Write the result 117896 at the end leaving 2 spaces to the right like this.
\begin{array}{c}\phantom{\times9999}29474\\\underline{\times\phantom{99999}3476}\\\phantom{\times999}176844\\\phantom{\times99}206318\phantom{9}\\\phantom{\times9}117896\phantom{99}\\\underline{\phantom{\times9}88422\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 29474 with 3. Write the result 88422 at the end leaving 3 spaces to the right like this.
\begin{array}{c}\phantom{\times9999}29474\\\underline{\times\phantom{99999}3476}\\\phantom{\times999}176844\\\phantom{\times99}206318\phantom{9}\\\phantom{\times9}117896\phantom{99}\\\underline{\phantom{\times9}88422\phantom{999}}\\\phantom{\times}102451624\end{array}
Now add the intermediate results to get final answer.