"Sie mag seinen Hund."

Translation: She likes his dog.

[sthosdkane]

Does the pronoun change based upon the noun it is in front of or the subject of the sentence? I was under the impression it was the former, but all of the incorrect answers that I've been putting in appear to show that it's the latter.

[az_p]

See my explanation here.

The pronoun has a 'front part' and an 'ending'. The 'front part' is chosen based on who the thing belongs to: sein- means the thing belongs to a male/neuter person/thing. The 'ending' is chosen based on the gender and case of the thing itself: -en is required for masculine nouns (such as Hund) in accusative case.

Other possible sentences to illustrate this:

Sie mag seinen Hund = "She likes his dog"
Sie mag seine Katze = "She likes his cat"
Sie mag ihren Hund = "She likes her dog"
Sie mag ihre Katze = "She likes her cat"
Er mag seinen Hund = "He likes his dog"
Er mag seine Katze = "He likes his cat"
Er mag ihren Hund = "He likes her dog"
Er mag ihre Katze = "He likes her cat"
Ihr mögt unsere Kuchen = "You like our cakes"
...

Don't be confused by the fact that the pronoun doesn't match the subject - in German as in English that can be ambiguous if they match, but they obviously don't have to:
"He likes her cat" = He likes the cat belonging to some other woman.
"He likes his dog" = He likes his own dog, or he likes the dog belonging to some other man.

[mizinamo]

The front part is just sein- without the -e-; (e.g. sein Pferd).

[az_p]

Thanks. Score 1 to autocorrect for the day. Fixed.

[ZacharyOro5]

Probably a useless question, but would "Hound" also translate to "Hund"?

[mizinamo]

No. "Hound" usually refers to a particular type of dog: a kind used for hunting. Thus a Jagdhund "hunt-dog".