At the Greenpoint Summer Festival, Farid is selling his animal-shaped cupcakes. Farid had to buy the ingredients and pay a food-vendor fee, so he hopes he sells enough cupcakes to make a profit.

To determine if \( x \) (the number of cupcakes) and \( y \) (the profit) have a proportional relationship, we need to check if the ratios \(\frac{y}{x}\) are constant for all pairs of \((x, y)\).

Let's calculate the ratios for the given points:

1. For \( x = 52 \) and \( y = 34 \): \[ \frac{y}{x} = \frac{34}{52} \approx 0.6538 \]

2. For \( x = 54 \) and \( y = 42 \): \[ \frac{y}{x} = \frac{42}{54} \approx 0.7778 \]

3. For \( x = 63 \) and \( y = 78 \): \[ \frac{y}{x} = \frac{78}{63} = 1.2381 \]

4. For \( x = 66 \) and \( y = 90 \): \[ \frac{y}{x} = \frac{90}{66} \approx 1.3636 \]

Since the ratios are not constant (they are approximately 0.6538, 0.7778, 1.2381, and 1.3636), we conclude that \( x \) and \( y \) do not have a proportional relationship.

Therefore, the answer is no.