The easiest way to answer quickly this question is to use your GDC and specifically the MOD which gives the remainder of a division.
For CASIO FX-9860GII do the following
RUN>OPTION>NUM>MOD
and you’ll find that the remainder when [tex]6^2 \cdot 4^2 is divided by 7 is 2, so the correct answer is (C).
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