In short, combinatorics is difficult because there is no easy, ready-made algorithm for counting things fast. You need to identify patterns/regularities offered by the particular problem at hand, and exploit them in a clever way to break down the big counting problem into smaller counting problems.

How difficult is combinatorics?

Combinatorics is, arguably, the most difficult subject in mathematics, which some attribute to the fact that it deals with discrete phenomena as opposed to continuous phenomena, the latter being usually more regular and well behaved.

How do I get better at combinatorics problems?

The key to solving a combinatorics problem is to find a systematic way to list the objects you want to count. Sometimes one first has to list these objects and some others, excess one. One then subtracts the excesss amount or divides out the excess factor.