Here's how the principle works. Say you're building a house, and you have two types of roof to choose from, and three types of windows, and that's all you're concerned about. So the number of ways to choose roof and windows is 2*3 = 6.
You can list them to see why. Say roofs are either A = angled, F = flat. Windows are either O = opaque, T = translucent, C = clear. (Yes, opaque windows are silly, but this is just an example.) Then the 6 possibilities are:
Please try to apply this principle to the problem. The follow-up problem with chicken and lettuce is a little more involved, but if you don't understand the counting principle it's useless to try to explain anything that builds on it.