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\begin{array}{c}\phantom{\times999}843453\\\underline{\times\phantom{99}5352655}\\\end{array}
First line up the numbers vertically and match the places from the right like this.
\begin{array}{c}\phantom{\times999}843453\\\underline{\times\phantom{99}5352655}\\\phantom{\times99}4217265\\\end{array}
Now multiply the first number with the 1^{st} digit in 2^{nd} number to get intermediate results. That is Multiply 843453 with 5. Write the result 4217265 at the end leaving 0 spaces to the right like this.
\begin{array}{c}\phantom{\times999}843453\\\underline{\times\phantom{99}5352655}\\\phantom{\times99}4217265\\\phantom{\times9}4217265\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 843453 with 5. Write the result 4217265 at the end leaving 1 spaces to the right like this.
\begin{array}{c}\phantom{\times999}843453\\\underline{\times\phantom{99}5352655}\\\phantom{\times99}4217265\\\phantom{\times9}4217265\phantom{9}\\\phantom{\times}5060718\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 843453 with 6. Write the result 5060718 at the end leaving 2 spaces to the right like this.
\begin{array}{c}\phantom{\times999}843453\\\underline{\times\phantom{99}5352655}\\\phantom{\times99}4217265\\\phantom{\times9}4217265\phantom{9}\\\phantom{\times}5060718\phantom{99}\\\phantom{\times}1686906\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 843453 with 2. Write the result 1686906 at the end leaving 3 spaces to the right like this.
\begin{array}{c}\phantom{\times999}843453\\\underline{\times\phantom{99}5352655}\\\phantom{\times99}4217265\\\phantom{\times9}4217265\phantom{9}\\\phantom{\times}5060718\phantom{99}\\\phantom{\times}1686906\phantom{999}\\\phantom{\times}4217265\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 843453 with 5. Write the result 4217265 at the end leaving 4 spaces to the right like this.
\begin{array}{c}\phantom{\times999}843453\\\underline{\times\phantom{99}5352655}\\\phantom{\times99}4217265\\\phantom{\times9}4217265\phantom{9}\\\phantom{\times}5060718\phantom{99}\\\phantom{\times}1686906\phantom{999}\\\phantom{\times}4217265\phantom{9999}\\\phantom{\times}2530359\phantom{99999}\\\end{array}
Now multiply the first number with the 6^{th} digit in 2^{nd} number to get intermediate results. That is Multiply 843453 with 3. Write the result 2530359 at the end leaving 5 spaces to the right like this.
\begin{array}{c}\phantom{\times999}843453\\\underline{\times\phantom{99}5352655}\\\phantom{\times99}4217265\\\phantom{\times9}4217265\phantom{9}\\\phantom{\times}5060718\phantom{99}\\\phantom{\times}1686906\phantom{999}\\\phantom{\times}4217265\phantom{9999}\\\phantom{\times}2530359\phantom{99999}\\\underline{\phantom{\times}4217265\phantom{999999}}\\\end{array}
Now multiply the first number with the 7^{th} digit in 2^{nd} number to get intermediate results. That is Multiply 843453 with 5. Write the result 4217265 at the end leaving 6 spaces to the right like this.
\begin{array}{c}\phantom{\times999}843453\\\underline{\times\phantom{99}5352655}\\\phantom{\times99}4217265\\\phantom{\times9}4217265\phantom{9}\\\phantom{\times}5060718\phantom{99}\\\phantom{\times}1686906\phantom{999}\\\phantom{\times}4217265\phantom{9999}\\\phantom{\times}2530359\phantom{99999}\\\underline{\phantom{\times}4217265\phantom{999999}}\\\phantom{\times}702289619\end{array}
Now add the intermediate results to get final answer.