To determine the value of $F(6)$ for the function $F(x) = 2^x$, we substitute $x = 6$ into the function:

$F(6) = 2^6$

We then calculate $2^6$:

$2^6 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 = 64$

Thus, the value of $F(6)$ is $64$.

The correct answer is:

$\boxed{\text{A. } 64}$

Would you like more details or have any questions?

Here are five more questions you might find useful to ask:

1. How do you evaluate exponential functions?
2. What are the properties of exponential functions?
3. How do you solve equations involving exponential functions?
4. What is the graph of $F(x)= 2^x$ and what are its key features?
5. How do exponential functions differ from linear functions?

Tip: When working with exponential functions, remember that they grow (or decay) at a rate proportional to their current value, which is different from the constant rate of change in linear functions.