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\begin{array}{c}\phantom{\times999}222\\\underline{\times\phantom{99}3457}\\\end{array}
First line up the numbers vertically and match the places from the right like this.
\begin{array}{c}\phantom{\times999}222\\\underline{\times\phantom{99}3457}\\\phantom{\times99}1554\\\end{array}
Now multiply the first number with the 1^{st} digit in 2^{nd} number to get intermediate results. That is Multiply 222 with 7. Write the result 1554 at the end leaving 0 spaces to the right like this.
\begin{array}{c}\phantom{\times999}222\\\underline{\times\phantom{99}3457}\\\phantom{\times99}1554\\\phantom{\times9}1110\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 222 with 5. Write the result 1110 at the end leaving 1 spaces to the right like this.
\begin{array}{c}\phantom{\times999}222\\\underline{\times\phantom{99}3457}\\\phantom{\times99}1554\\\phantom{\times9}1110\phantom{9}\\\phantom{\times9}888\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 222 with 4. Write the result 888 at the end leaving 2 spaces to the right like this.
\begin{array}{c}\phantom{\times999}222\\\underline{\times\phantom{99}3457}\\\phantom{\times99}1554\\\phantom{\times9}1110\phantom{9}\\\phantom{\times9}888\phantom{99}\\\underline{\phantom{\times}666\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 222 with 3. Write the result 666 at the end leaving 3 spaces to the right like this.
\begin{array}{c}\phantom{\times999}222\\\underline{\times\phantom{99}3457}\\\phantom{\times99}1554\\\phantom{\times9}1110\phantom{9}\\\phantom{\times9}888\phantom{99}\\\underline{\phantom{\times}666\phantom{999}}\\\phantom{\times}767454\end{array}
Now add the intermediate results to get final answer.