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\begin{array}{c}\phantom{\times999}121\\\underline{\times\phantom{99}3737}\\\end{array}
First line up the numbers vertically and match the places from the right like this.
\begin{array}{c}\phantom{\times999}121\\\underline{\times\phantom{99}3737}\\\phantom{\times999}847\\\end{array}
Now multiply the first number with the 1^{st} digit in 2^{nd} number to get intermediate results. That is Multiply 121 with 7. Write the result 847 at the end leaving 0 spaces to the right like this.
\begin{array}{c}\phantom{\times999}121\\\underline{\times\phantom{99}3737}\\\phantom{\times999}847\\\phantom{\times99}363\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 121 with 3. Write the result 363 at the end leaving 1 spaces to the right like this.
\begin{array}{c}\phantom{\times999}121\\\underline{\times\phantom{99}3737}\\\phantom{\times999}847\\\phantom{\times99}363\phantom{9}\\\phantom{\times9}847\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 121 with 7. Write the result 847 at the end leaving 2 spaces to the right like this.
\begin{array}{c}\phantom{\times999}121\\\underline{\times\phantom{99}3737}\\\phantom{\times999}847\\\phantom{\times99}363\phantom{9}\\\phantom{\times9}847\phantom{99}\\\underline{\phantom{\times}363\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 121 with 3. Write the result 363 at the end leaving 3 spaces to the right like this.
\begin{array}{c}\phantom{\times999}121\\\underline{\times\phantom{99}3737}\\\phantom{\times999}847\\\phantom{\times99}363\phantom{9}\\\phantom{\times9}847\phantom{99}\\\underline{\phantom{\times}363\phantom{999}}\\\phantom{\times}452177\end{array}
Now add the intermediate results to get final answer.