Sometimes they don't realize that you can add them, but often times they realize they are like terms but end up messing with the exponents. To me, it's really just a matter of how they are looking at it. My best attempt at getting my students to see this problem the way that I see it is by telling them that if everything in a term is the same except for the coefficient(1) is the same you can think of it as a banana. Therefore, the problem above is simply:
Now, they see the answer is 4, but don't totally get it right away, so the banana explanation is quickly followed by:
"So, when you add a banana and 3 bananas, does the fact that you're adding bananas change?"
"So the answer is 4 bananas, and what did we say was a banana?", etc
During that exchange the lightbulb goes off and they get it.
Just like the rainbow rule, I'll go through this with a class the first time time it comes up naturally in some problem, and then refresh it as it comes up throughout the year. This method seems to reinforce that it's a tool, and not just "this is how you do this kind of problem". If I have time, I might go off on a tangent about how it works with anything even if they haven't seen it before and go through some quick examples with trig, logs, integrals or crazy fractions and roots. Also like rainbow rule, it helps kids put a name to something they struggle with and attaches an intuitive process to it.
(1)Okay, I usually say "number in front" instead of coefficient at this juncture, but we're trying to make it simple right? Please let me keep my math teacher card.