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\begin{array}{c}\phantom{\times99}54654219\\\underline{\times\phantom{9999999}649}\\\end{array}
First line up the numbers vertically and match the places from the right like this.
\begin{array}{c}\phantom{\times99}54654219\\\underline{\times\phantom{9999999}649}\\\phantom{\times9}491887971\\\end{array}
Now multiply the first number with the 1^{st} digit in 2^{nd} number to get intermediate results. That is Multiply 54654219 with 9. Write the result 491887971 at the end leaving 0 spaces to the right like this.
\begin{array}{c}\phantom{\times99}54654219\\\underline{\times\phantom{9999999}649}\\\phantom{\times9}491887971\\\phantom{\times}218616876\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 54654219 with 4. Write the result 218616876 at the end leaving 1 spaces to the right like this.
\begin{array}{c}\phantom{\times99}54654219\\\underline{\times\phantom{9999999}649}\\\phantom{\times9}491887971\\\phantom{\times}218616876\phantom{9}\\\underline{\phantom{\times}327925314\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 54654219 with 6. Write the result 327925314 at the end leaving 2 spaces to the right like this.
\begin{array}{c}\phantom{\times99}54654219\\\underline{\times\phantom{9999999}649}\\\phantom{\times9}491887971\\\phantom{\times}218616876\phantom{9}\\\underline{\phantom{\times}327925314\phantom{99}}\\\phantom{\times}1110849763\end{array}
Now add the intermediate results to get final answer.