Step 1 :The problem is asking for the value of the function \(f(x) = 8^{x^{2}-6}-2\) when \(x=-2\).
Step 2 :To find this, we substitute \(x=-2\) into the function.
Step 3 :So, \(f(-2) = 8^{(-2)^{2}-6}-2\).
Step 4 :Solving this, we get \(f(-2) = -1.984375\).
Step 5 :Rounding to the nearest hundredth, we get \(-1.98\).
Step 6 :Final Answer: The value of \(f(-2)\), to the nearest hundredth, is \(\boxed{-1.98}\).