What is the difference between the probable Engel curves for European vacations and Cheapo brand sneakers at $9.99 per pair?
In essence, this question is asking which of these goods is a normal good and which is an inferior good. This is because Engel curves show the relationship between income and the quantity demanded of a good. This relationship determines whether a good is normal or inferior.
A normal good is one for which the demand increases as people come to have more income. On an Engel curve, this would be represented by a curve that goes up from left to right. Of the goods that you mention, European vacations would clearly be a normal good. The more money people have, the more likely they are to spend on something expensive and fancy like going to Europe for vacation.
An inferior good is one for which the demand decreases as income increases. Therefore, this will have an Engel curve that slants downward from left to right. At high incomes, the demand is low and at low incomes the demand is high. The Cheapo Brand sneakers would likely fall in this category. They would probably be seen as something that people buy only when they must. If people have more money, they will buy some other brand of sneaker that is more expensive and, presumably, of higher quality.