You are going to mix a gallon bucket of window cleaner. the instructions direct you to mix 1 part cleaner to 3 parts water. how much cleaning solution will you need to use?

You have a bucket 1 gallon big.
To mix cleaner and water you need to divide the bucket's capacity into 4.
It's easy in this case as gallon is divided into quarts (1 gallon is equal to 4 quarts).
Since one part will be a window cleaner, it means that you will need to use 1 quart of the cleaner.  

Is there a picture of a graph or whatever that goes along with this?

The answer is why would a teacher ask that