How do you figure out how many cups are in 6 liters using dimensional analysis?
First you need to find an equality between cups and Liters. A Google search determined that 1 L = 4.22675 US cups.
Next, you need to determine the conversion factors from this equality.
Because the numerators equal the denominators, the conversion factors = 1, so when you multiply your given volume times the correct conversion factor, you are not changing the volume, just the units for the volume.
You need to multiply 6 L times the conversion factor with Liters on the bottom and cups on top. This will cancel the Liters and leave you with cups.