"The old house looks different from what I remember."
"The old house looks different than what I remember."
"The old house looks different than I remember."
"The old house looks different from I remember."
*I am not 100% certain about this, but the norm is that "than" is usually used with comparative adjectives...smaller than, larger than, crazier than, etc.
In this case the word "different" isn't a comparative adjective. So "different from what I remember" is the preferred construct, but the exceptional insertion of "than" in this instance allows the sentence to be more flexible for the addition/subtraction of "what."
Additionally, "from I remember" as a phrase wouldn't be correct, I think because there is no object to the preposition. The word "what" becomes the object.
I speak English fluently and I enjoy challenges like this question a lot, but it still took me a really long time to get to this answer, which is not difinitive, and it did not come without help. So if you want to keep it slightly more simple, you can think of it this way:
*You can either use the phrase "from what" to prompt a comparison statement OR you can use the word "than."
I love your questions. I learn so much from them!