To compare \( f(2) \) and \( g(2) \), we first need to evaluate both functions at \( x = 2 \).
Given the functions:
- \( f(x) = 4x \)
- \( g(x) = 6 \cdot 2^x \)
Calculating \( f(2) \):
\[ f(2) = 4 \cdot 2 = 8 \]
Now, calculating \( g(2) \):
\[ g(2) = 6 \cdot 2^2 = 6 \cdot 4 = 24 \]
Now, we can compare:
\[ f(2) = 8 \quad \text{and} \quad g(2) = 24 \]
Since \( 8 < 24 \), we can conclude that:
\[ f(2) < g(2) \]
Therefore, the correct answer is:
\( f(2) < g(2) \).