It was quite clear that this place was not big enough to house all the family members.
-between the two sentences below, Which one has the same meaning as the one above?
It was quite cleat that this place was not so big that it could house all the family members
It was quite clear that this place was not so big that it couldn't house all the family members
I'm assuming "It was quite cleat" is a typo, and should be "It was quite clear". The first of your two sentences has the same meaning as your first statement. The second uses a "double negative; - "not" and "couldn't" which effectively, cancel each other out. The second sentence actually means, that it could house all the family members.
The use of two negatives, which cancel each other out.
"a syntactic construction in which two negative words are used in the same clause to express a single negation."
"He didn't say nothing" MEANS- He said something.
"I ain't not never gunna do it" MEANS- I will do it.
"There is not nobody who will go" MEANS- Someone will go.
"I don't want nothing" MEANS- I want something.
"We don't need no education" MEANS- We need education.If a man did not say nothing, that means he said something.
From a logical point of view, two negative cancel each other out, and produce a positive meaning. This is not how language works all the time, though.
Pedants will point out what they see as a flaw in logic when you tell them I didn't see nothing: it can be parsed as I saw something. In real life, however, that utterance will more often be interpreted (and intended!) to mean I din't see anything.
So when does a double negative work? It depends on context and semantics. If I look at one of @RobynSimpson's examples, the context is very important:
We don't need no education
We don't need no thought control
No dark sarcasm in the classroom
Teachers leave them kids alone
Hey! Teachers! Leave them kids alone
These lines are from Pink Floyd's Another brick in the wall.
The two first lines both contain a double negative, but their meaning is not positive. The context makes it quite clear that those lines do not mean "we need education, and we need though control".
So, did Pink Floyd mess up their language or grammar?
No, this construction is incredibly common (the Rolling Stones sang I can't get no satisfaction) and in everyday use, I didn't do nothing is often considered acceptable in non-formal registers.
Now, let's have a look at your second option:
It was quite clear that this place was not so big that it couldn't house all the family members.
Clearly, your first option is logically and grammatically the one that conveys the same meaning as your original sentence, but your second option can be read as having the same meaning!
I do admit the sentence is a bit confusing, and I would advise against using it like this. However, I have come across sentences like this in real life, and parsed them as having a negative meaning based on semantics.
Why would I say the house was not so big - basically saying it was big - but not to the extend that it could not house the whole family? That is a non-sequitur, leading me to believe the second negation is only there for emphasis, meaning that indeed, the two negatives are not cancelling each other out.
A semantically different statement would lead me to believe the two negative are meant to form a positive:
It was quite clear that this place was not so small that it couldn't house all the family members.
In this case I would certainly parse the sentence to mean that the house is big enough for a whole family.
