Translation:I met the owner of the house a year ago.
If by 'met with' you mean something like 'had a meeting/appointment with' (as opposed to making his acquaintance), that'd probably be я встретился с ...
"I met the owner of the home a year ago" - should be accepted, and reported
I believe it should be accepted too. Please use the 'Report' button next time you get this sentence.
I put "met the homeowner..." but after reading your comment I think maybe both of our answers are a little more specific than the Russian sentence. "Landlord" specifies a rental property, while "homeowner" has connotations that the owner lives there; it is his home, not just his house. I don't know for sure but I sense the Russian sentence is more neutral.
It’s a possible meaning.
In speech, this would be distinguished by intonation (in your version, дома would receive more emphasis), but there is no real way to distinguish them in writing. But «хозяин дома» is a common phrase, so the meaning suggested by Duolingo is much more likely than yours.
I think this choice should be accepted. Report it next time you will come across this task.