Multiply and round to the proper number of significant figures. (0.234 cm)(3.53 cm)

Best   Using a calculator, it's easy to get the answer of 0.82602 cm^2. 

When it says "proper number of significant figures", that just means the accuracy of the answer can only be equal to the accuracy of the original data. So since 0.234 and 3.53 are both only accurate to 3 s.f. the answer must also be accurate to 3 s.f. 

So the final answer you get is 0.826 cm^2.