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\begin{array}{c}\phantom{\times999}30\\\underline{\times\phantom{99}556}\\\end{array}
First line up the numbers vertically and match the places from the right like this.
\begin{array}{c}\phantom{\times999}30\\\underline{\times\phantom{99}556}\\\phantom{\times99}180\\\end{array}
Now multiply the first number with the 1^{st} digit in 2^{nd} number to get intermediate results. That is Multiply 30 with 6. Write the result 180 at the end leaving 0 spaces to the right like this.
\begin{array}{c}\phantom{\times999}30\\\underline{\times\phantom{99}556}\\\phantom{\times99}180\\\phantom{\times9}150\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 30 with 5. Write the result 150 at the end leaving 1 spaces to the right like this.
\begin{array}{c}\phantom{\times999}30\\\underline{\times\phantom{99}556}\\\phantom{\times99}180\\\phantom{\times9}150\phantom{9}\\\underline{\phantom{\times}150\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 30 with 5. Write the result 150 at the end leaving 2 spaces to the right like this.
\begin{array}{c}\phantom{\times999}30\\\underline{\times\phantom{99}556}\\\phantom{\times99}180\\\phantom{\times9}150\phantom{9}\\\underline{\phantom{\times}150\phantom{99}}\\\phantom{\times}16680\end{array}
Now add the intermediate results to get final answer.