"Raj lives in your home."
Translation:राज तेरे घर में रहता है।
The noun phrase 'तेरा घर' is in the oblique case in this sentence because it is the object of the postposition 'में'. The oblique form of 'तेरा घर' is 'तेरे घर' which is why the latter should be used. (The plural form of तेरा to be used for a plural object is also तेरे but the two instances should not be confused).
Similarly, if you use the formal forms, तुम्हारा or आपका, they would still be in the oblique case so the sentences are राज तुम्हारे घर में रहता है। and राज आपके घर में रहता है।
This is the literal translation.
राज - 'Raj'
तेरा घर - 'your home'
तेरे घर में - 'in your home' (because Hindi uses postpositions, unlike English which uses prepositions.
रहता - form of the verb रहना - 'to live'
रहता है - 'lives' (है is an auxiliary verb which indicates that the sentence is in the present tense
Hindi sentences are usually ordered subject-object-verb.
So, राज तेरे घर में रहता है। - Raj lives in your home.