- I don't like the computer gifted to me by my father that doesn't have enough RAM.
- I don't like the computer that doesn't have enough RAM gifted to me by my father.
Can I use these sentences?
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Please see my answer to your earlier question.
Neither sentence is clear.
The first seems to say you don't like the computer your father, who hasn't enough RAM, gave you.
The second says your father gave you some RAM. It was installed into at least two computers but one of them didn't get enough and you don't like that one.
I agree with Jack's solutions. They are what I would say. Neither of them uses "that", btw.
It is possible to write grammatically-correct sentences that are confusing or meaningless. Clarity is what we need!