Expanding something out like (x+2)(x+3) crops up everywhere in maths. Therefore it's a very important skill to develop.

There are many different ways of looking at it - smily faces, rainbows, claws - to name a few, and everyone has their favourite. However, all of them essential boil down to multipling everything in the first bracket with everything in the second bracket. 

A good first way to look at it is to expand the first bracket to begin with. Taking our example at the top, we get (x+2)(x+3) = x(x+3) + 2(x+3). 

We can then expand these as individual brackets: x² + 3x + 2x + 6.

Finally, we can collect like terms to simplify: x² + 5x + 6

And we're done. With practise, this becomes one of those things you do so often, you almost stop thinking about it. Until someone asks you what your favourite method is and then the arguments begin...