What and How

[Planetypus]

I am an English teacher, but I am not an English-major graduate. I am teaching beginners to the English language but some of my students are so inquisitive. I am sometimes confused with what to answer them. This forum has really helped me a lot.

Today, one of my students asked me, "When do we use what and how in situations like, What a beautiful house and How beautiful?"

I was confused. I told her that I had to think for a while. Later, I told her that we can use what when we use the articles a/an and how when we don't. Additionally, I said, "We don't use nouns after the adjective when we use how, or we could rearrange the words."

Examples:

What a huge garden!
How huge! or How huge a garden!

Now, my question is: Was everything I told her correct?
If not, I want some clarification about this matter. Can anybody help me, please?

Thanks a lot!

[Mister Micawber]

.
Seems good to me, offhand. Notice the case of the plural noun, though-- no article:

How beautiful you are!
How beautiful your gardens are!
How beautiful a garden you have!

What a beautiful garden you have!
What beautiful eyes you have!

What a beauty you are! (noun)
What beauties they are!
.
_________________
Canadian-American native speaker
who teaches English for a living at Mister Micawber's
ESL cafe: Interview with Mister Micawber

[Planetypus]

I get a lot of things from your response. Thanks a lot.