Here is a more complicated example using not just conversion factors be physical/chemical entities such as density and molar mass. How many moles is 15 gallons (about 1 tank) of gasoline? The density of gasoline is 0.75kg/L. The molar mass of gasoline is 114.22g/mol.
Upon reading the problem careful we notice that our starting number is 15 gallons (a measurement and not a conversion factor). The final answer should be in moles. At this point in the course you don't really know what moles are. But it doesn't matter. You are given a conversion factor to go from grams to moles. So if you can get to grams you can get to moles. Notice that your given units are a unit of volume, but somehow you need to get to grams, a mass unit. This will involve the density, the property that relates the mass of a substance to its volume. We will also need a gallons to liter conversion (look this up) and a kilograms to gram conversion (an SI prefix that you should have memorized).
First enter 15 gallons in the Initial Value (the pink boxes). To use the given density "conversion factor" we need to get to Liters. That will put us in kilograms. Then to use the molar mass "conversion factor" we need to get to grams.
Enter these into the calculator so that the denominator has the units of the previous term's numerator. Notice that gallons cancel, Liters cancel, kilograms cancel, and grams cancel, and that you are left with just moles. You should get 372 mol (to 3 significant figures). For what it's worth right now. 372 moles tells us how many gasoline molecules we have (372 x Avogadro's number, which is 6.02 x 1023 molecules).