If you could increase your number of hours to 48/week, it will help you become a more fluent speaker.
If you can increase your number of hours to 48/week, it will help you become a more fluent speaker.
The first sentence sounds more natural to me. Which one is correct and why?
I think I'd be happier with the first sentence if it was written as:
If you could increase your number of hours to 48/week, it would help you become more fluent.
It maintains the same set of auxilliary verbs in both halves of the sentence. It is also a bit passive, compared with the more active second sentence:
If you can increase your number of hours to 48/week, it will help you become a more fluent speaker.
I'd choose between them on the basis of my expectation of the increase happening; the first has a resigned air to it (if you could, you would, but you probably can't, so you won't), whereas the second is more positive (if you can, you will, and since you can, you will improve) or authoritative (an order disguised as a suggestion).
I think "if you could" means "if you are able to/have time to".
And "if you can" seems more like "if you are capable of".
I also feel that the first sentence sounds better and more natural.
Actually the first one sounds odd to me. I'd say it's rather like this:
(1) If you could increase your number of hours to 48/week, (2) it would help you become a more fluent speaker.
It's a sentence (in Linguistic meaning) made of two clauses: The main one is the #2, the subordinate is the #1 and it's a conditional clause. (=If the condition becomes true, the proposition in the main clause will realize.)
I think the other one is basically the same:
If you can increase your number of hours to 48/week, it will help you become a more fluent speaker.
They sound a bit different about "your feeling" regarding their actual realisation, since you use "could/would" in the first and "can/will" in the second.
