Mathemtical Economics Question regarding Profit Maximization
Well, it's very straightforward question. You have a cost function, from which you can get a Supply Curve, by taking its first derivative. You'll find competitive price and quantity when the supply curve you got meets the demand curve. 

First, our supply curve: $$P = 4Q$$
Then, the demand curve:

$$ P = 32- 2Q$$

Competitive $Q$ is:

$$ 32 - 2Q = 4Q $$
$$Q = \frac{32}{6} \approx 5.333$$

So, competitive price is: 
$$ P = 32 - 2 * 5.333 \approx 21.333$$