To get this answer, you simply multiply out all the values given. So we have 2*4*7*4 = 8*28 = 224. The reason why this works is to imagine we only had two aspects to focus on. Let's say we could only choose 2 sizes and 4 colors. Lay out a table that has 2 rows and 4 columns. This table will have 2*4 = 8 different cells inside it to represent the 8 different combinations possible. This idea can be extended to more dimensions than just two, though it might be tricky to visualize. Another way to see this is to draw out a tree diagram. Unfortunately with large numbers such as this, the tree diagram gets very unwieldy. In your math book, this concept may be referred to as the "counting principle".
