The correct option is
A Shyla invited me home, but I did not go there as I was not comfortable.
A simple sentence has only one subject and predicate. It has a finite verb with a completed thought. A compound sentence has at least two parts (also referred to as a clause). Each part has its own subject and predicate and makes good sense by itself. Hence each clause is independent of the other and called the main clause or independent clause. The main clauses are connected using a co-ordinating conjunction (for, and, nor, but, or, yet, so).A complex sentence has at least one main clause (which is an independent clause) and one or more dependent clauses, connected using a subordinate conjunction. The dependent clause cannot stand by itself and make good sense. It depends upon the main clause.
Option A: The three clauses viz (i) "Shyla invited me home", (ii) "I did not go there" and (iii)" I was not comfortable" can stand independently and make good sense. They are independent clausesconnected using the co-ordinating conjunctions-"but" and "as". Hence, this is a compound sentence and this answer is correct.
Option B: The words, "though" and "as" are subordinating conjunctions which connect independent and dependent clauses. The clauses, "I did not go there" is an independent clause. However, the clauses, "Though Shyla invited me home" and "as I was not comfortable" cannot stand on their own and make good sense. They are dependent clauses. Hence, this is a complex sentence and this option is incorrect.
Option C: The clause, "I did not go there" is an independent clause. The words, "due to discomfort" and "Inspite of Shyla inviting me home" are both phrases and not clauses. Hence, this is a simple sentence and this option is incorrect.
Option D: The word "uncomfortable" describes the subject "I". However, in option D, it describes the noun, "home". Hence, this sentence no longer conveys the original meaning. Further, the words, "So that" is a subordinating conjunction which connect independent and dependent clauses. The clause, 'so I did not go there" does not make good sense on its own and is a dependent clause. Hence, the sentence is a complex sentence and this option is incorrect.