Which is correct: "a hour" or "an hour"?

I am an English teacher, maybe I could enlighten you a bit.
First thing first, to decide whether it’s a/an to a word, it all depends on how we pronounce the word itself. If we pronounce the word, and the first sound starts with vowels (a,i,u,o,e) you give ‘an’.
Let’s take it from the word ‘Apple’. We pronounce it as /eipel/ give or take. It comes off from letter ‘e’ which is vowels, so we use ‘an’, ‘an apple’ not ‘a apple’.

Now, if we are pronouncing a word and it starts from any letter besides vowels, you put ‘a’, like, ‘bag’ /beg/, it starts ‘b’ so we put ‘a bag’ not ‘an bag’.

For the word ‘Hour’, the correct pronunciation is /auer/ more or less. The first letter we hear is ‘a’ which is a vowel, so we put ‘an hour’ not ‘a hour’. I am giving you more example.

Let’s take a look at the word ‘University’, to pronounce it, you say /yuniversiti/.
Having said that, the very first letter you her is /y/ so you do not put ‘an university’, but ‘a university’.

--------------------- Good luck