To determine the equation that represents the relationship between the cost of cookies (y) and the number of cookies bought (x) during the sale, we need to first find the new price per cookie after the $0.10 discount.
Initially, the baker sells 4 cookies for $2. Therefore, the price per cookie is:
\[ \text{Price per cookie} = \frac{2}{4} = 0.50 \text{ dollars} \]
During the sale, he is charging $0.10 less per cookie:
\[ \text{Sale price per cookie} = 0.50 - 0.10 = 0.40 \text{ dollars} \]
Now, if x represents the number of cookies purchased, the total cost (y) can be expressed as:
\[ y = \text{(price per cookie)} \times x = 0.40x \]
Thus, the equation that represents the cost (y) based on the number of cookies (x) bought during the sale is:
\[ \boxed{y = 0.40x} \]
So, the correct choice is (c) \(y = 0.40x\).