To solve the given expression, we need to follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)). First, calculate the exponent \((-4)^3\), then evaluate the expression inside the parentheses. Next, compute the denominator \(4^2 - 2 \cdot 3\). Finally, divide the results and raise the quotient to the power of 2.
First, calculate the exponent \((-4)^3\):
\[
(-4)^3 = -64
\]
Substitute the result from Step 1 into the numerator:
\[
6 - (-4)^3 = 6 - (-64) = 6 + 64 = 70
\]
Calculate the denominator:
\[
4^2 - 2 \cdot 3 = 16 - 6 = 10
\]
Divide the results from Step 2 and Step 3:
\[
\frac{70}{10} = 7
\]
Raise the result from Step 4 to the power of 2:
\[
7^2 = 49
\]