This problem calls for use of the Fundamental Counting Principle, they have a video in the algebra section (I think) that explains it better than I probably could, but I'll try to sum up.
Every catergory of choice can be represented by the number of choices you could potentially make, and when you multiply all of the numbers of choiices together, that is the max possible number of unique combinations among the group. For instance, if you throw two different color dice, with six possible outcomes on each die, there are 6 times 6 possible combinations of results. For your problem there are 8 * 5 * 10 * 4 = 1600 possible combinations.
Another way to look at solving the problem is with an outcome tree. In our dicxe problem, you could take one color and write out the six possible outcomes. Then, branching off each potential outcome you set each possible result from the other/next die. When all the ptions have been layed out, count how many endpoints you have, that’s how many choice paths or combinations of choices, are available.
One can see quickly that with the clothing question, ten shirts start the tree, with eight pairs of pants branching off each. This gives us eighty shirt/pants combinations to apply each tie to, for 400 possible outfits, then there are four versions of each outfit, depending on yer shoes, 1600 possible outfits.