To apply the Quotient Rule of Exponents, you subtract the exponent in the denominator from the exponent in the numerator. The rule states that:
\[ \frac{a^m}{a^n} = a^{m-n} \]
In your case, we have:
\[ \frac{2^6}{2^2} = 2^{6-2} \]
Calculating that gives:
\[ 2^{4} \]
Therefore, the equivalent expression is \( 2^4 \), which is not listed in your response options. However, it seems that I misjudged your options. Let’s review the provided options for correctness.
The multiple-choice answers have \( 2^3 \), \( 2^8 \), \( 2^{12} \) as the variations to choose from. Revisiting and rectifying based on our first principles, the correct equivalent expression derived was \( 2^4 \), confirming no direct match among the options.
Please check the choices again, and if you're seeking the nearest possible value for understanding, the confirmatory choice might lay around \(2^{(6-2)=4}\).
If this wasn't to be among your targeted selections, please provide clarity or appraise for different expressions.