Difference between "would have" and "would" in the following

Solution 1:

The first thing to say is that ‘By the time I would realize . . .’ is not grammatical. You need ‘By the time I realized it . . .’

As for the main clause, ‘four hours had passed’ is, as the previous post suggests, the best solution. If you want to use ‘would’ for some reason, it would have to be something like ‘Every once in a while I would go this friend's house and we would get into a discussion. By the time I realized it, the entire visit would have taken 4 hours.'

Solution 2:

They both use would four times, which is odd, but I see what you're driving at.

Edit: to explain the differences as I see them:

the first way:

Every once in a while I would go to this friend's house and we would get into a discussion.

You begin describing a series of events that all occurred in the past.

By the time I would realize,

but once you've said this, you're describing a future possibility, which disagrees with the tense of your introduction.

For example, I don't live close enough to the office to go home for lunch. By the time I would get to my apartment, I would have to turn around and go back to work.

That said, you can't use realize on its own in this context. You need to use it, which you do:

it would have taken 4 hours.

but it should immediately follow realize.

Bottom line, the first sentence wins. Would have taken is correct, because it keeps you in the past.

However, may I suggest:

Every once in a while I would go this friend's house and we would get into a discussion. Before I knew it, four hours had passed.