First, let's look at the fundamental properties of matter:
- mass - This is what we perceive as weight although weight is actually a derived unit of force (that is, mass times the acceleration of gravity = weight). Basic SI units of mass are grams (g).
- length - Pretty self-explanatory. The basic SI unit of length is the meter (m).
- Some others include temperature, charge, and spin (for subatomic particles).
From these fundamental units can be derived many other units. For example, length can be used to derive area (square meters, square centimeters, etc) or volume (cubic meters, cubic centimeters, liters, milliliters, etc).
Density is another derived property. It is a measure of the mass per unit volume. Density relates volume and mass. If you know any two of them, you can always calculate the third because D = m/V.
In your case, you're given the density (0.67 g/ml) and the volume (18 gal) and are asked to calculate the weight in kilograms (which is, strictly speaking, a unit of mass but we'll just let it stand as is).
- Convert your given volume units (gallons) to units consistent with your given density (ml). 18 gal x 3785.4 ml/gal = 68137.2 ml
- Solve equation D=m/V for mass: m = D x V
- Substitute numerical values into #2: (0.67 g/ml x 68137.2 ml = 45651.9 g)
- Convert the answer in #3 from grams to kilograms: 45651.9 g x (1 kg/1000 g) = 46 kg (using 2 sig fig since volume was given to 2 sig fig)
(Strictly speaking, what we've calculated is the mass of the gasoline. Its weight would actually be found by multiplying that mass by the acceleration of gravity. Unfortunately, many people outside of the physics world get pretty sloppy with the mass / weight distinction.)