Solve for the value of 3^a-b given 2^a = 16 and 2^b = 4.

We are given the equation $2^a = 16$.
We can express 16 as a power of 2: $16 = 2 \times 2 \times 2 \times 2 = 2^4$.
So, we have:

$$2^a = 2^4$$

Equating the exponents, we find:

$$a = 4$$

We are given the equation $2^b = 4$.
We can express 4 as a power of 2: $4 = 2 \times 2 = 2^2$.
So, we have:

$$2^b = 2^2$$

Equating the exponents, we find:

$$b = 2$$

Now that we have the values for $a$ and $b$, we can find their difference:

$$a - b = 4 - 2 = 2$$

Substitute the value of $a-b$ into the expression $3^{a-b}$:

$$3^{a-b} = 3^2$$ $$3^2 = 3 \times 3 = 9$$

The final answer is $\text{9}$.