Can you tell us where you have trouble understanding it? Otherwise, you're just asking us to say the same thing in a different way, without knowing what parts need to be changed.
Briefly, I might think this way: You are given two ratios that are equal to 1 (that is, numerator and denominator represent the same quantity):
3.79 liters/1 gallon, 3.36 dollars/1 gallon
You want the number of dollars per liter. So you want to multiply together fractions such that dollars will be on top (3.36 dollars/gallon is fine) and liters will be on the bottom (3.79 liters/gallon is upside-down).
So we can flip the second fraction: \(\displaystyle \displaystyle \frac{3.36\ \text{dollars}}{1\ \text{gallon}} \cdot \frac{1\ \text{gallon}}{3.79\ \text{liters}}\). The gallons will "cancel" just like when you multiply ordinary fractions, leaving \(\displaystyle \displaystyle\frac{3.36\ \text{dollars}}{3.79\ \text{liters}}\).
This means we divide 3.36 by 3.79, and the answer is 0.8865 dollars/liter, which rounds to $0.89.
Note that the wrong answers involve either dividing in the wrong order, or rounding incorrectly, so those appear to be the ideas they are testing.
This is not the only way to solve the problem; frankly, it is a good way largely because it does away with thinking! But another way to do it would be to think about the meaning of the ratios. We want the price for one liter. We know that 3.79 liters make a gallon; one liter is 1/3.79 of a gallon. We know that one gallon costs $3.36; 1/3.79 gallon costs 1/3.79 as much. So we have to multiply $3.36 by 1/3.79, which means dividing $3.36/3.79.
There are lots of other ways, so if you think of a way that makes sense to you because of your particular experiences, try it.