c) $\lim _{x \rightarrow 2} \frac{\sqrt[3]{(x+6)}-2}{x-2} \cdot \frac{\sqrt[3]{(x+6)}+2}{\sqrt[3]{(x+6)}+2}$

Step 1 ：\(\text{Simplify the expression by multiplying the two fractions:}\)

Step 2 ：\(\frac{\sqrt[3]{(x+6)}-2}{x-2} \cdot \frac{\sqrt[3]{(x+6)}+2}{\sqrt[3]{(x+6)}+2} = \frac{(\sqrt[3]{(x+6)}-2)(\sqrt[3]{(x+6)}+2)}{x-2}\)

Step 3 ：\(\text{Find the limit as x approaches 2:}\)

Step 4 ：\(\lim_{x \rightarrow 2} \frac{(\sqrt[3]{(x+6)}-2)(\sqrt[3]{(x+6)}+2)}{x-2}\)

Step 5 ：\(\text{The limit as x approaches 2 is infinity.}\)

Step 6 ：\(\boxed{\infty}\)