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\begin{array}{c}\phantom{\times}555666\\\underline{\times\phantom{}6525}\\\end{array}
First line up the numbers vertically and match the places from the right like this.
\begin{array}{c}\phantom{\times}555666\\\underline{\times\phantom{}6525}\\\phantom{\times}2778330\\\end{array}
Now multiply the first number with the 1^{st} digit in 2^{nd} number to get intermediate results. That is Multiply 555666 with 5. Write the result 2778330 at the end leaving 0 spaces to the right like this.
\begin{array}{c}\phantom{\times}555666\\\underline{\times\phantom{}6525}\\\phantom{\times}2778330\\\phantom{\times}1111332\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 555666 with 2. Write the result 1111332 at the end leaving 1 spaces to the right like this.
\begin{array}{c}\phantom{\times}555666\\\underline{\times\phantom{}6525}\\\phantom{\times}2778330\\\phantom{\times}1111332\phantom{9}\\\phantom{\times}2778330\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 555666 with 5. Write the result 2778330 at the end leaving 2 spaces to the right like this.
\begin{array}{c}\phantom{\times}555666\\\underline{\times\phantom{}6525}\\\phantom{\times}2778330\\\phantom{\times}1111332\phantom{9}\\\phantom{\times}2778330\phantom{99}\\\underline{\phantom{\times}3333996\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 555666 with 6. Write the result 3333996 at the end leaving 3 spaces to the right like this.
\begin{array}{c}\phantom{\times}555666\\\underline{\times\phantom{}6525}\\\phantom{\times}2778330\\\phantom{\times}1111332\phantom{9}\\\phantom{\times}2778330\phantom{99}\\\underline{\phantom{\times}3333996\phantom{999}}\\\phantom{\times}-669246646\end{array}
Now add the intermediate results to get final answer.