A compound sentence is a sentence containing two or more independent clauses (complete sentences), joined by a coordinating conjunction.
"I went home early" is a complete sentence with a subject (I), a verb (went), a direct object (home), and an adverb (early) which modifies the verb.
The independent clauses of a compound sentence should be related in some way.
Examples of compound sentences:
I went home early but I forgot my assignment book.
- two independent clauses joined by the conjunction 'but'.
I wasn't feeling well so I went home early.
- two independent clauses joined by the conjunction 'so'.
I went home early since it was a half day.
Because it was a half day, I went home early.
- joined by the coordinating conjunctions 'since' and 'because'.
Note that the two independent clauses can be in the reverse order with a comma separating them. The coordinating conjunction can start the sentence.
I went home early and washed my hair.
NOT a compound sentence. The second part of the sentence has no subject of its own.
The conjunction 'and' is joining the compound verb.