Questions & Answers about Мы хотим продать этот дом.
Why didn't этот дом change its ending if it is the direct object of the verb?
Because дом is a masculine inanimate noun (a non-living thing). In the accusative case (used for direct objects), inanimate masculine nouns and their modifiers (like the demonstrative pronoun этот) look exactly the same as they do in the nominative dictionary form. If it were a living masculine noun like brother (брат), the phrase would change to этого брата.
Why do we use продать here instead of продавать?
Продать is the perfective aspect of the verb to sell. It is used here because the goal is a single, successfully completed result: getting the house sold once and for all. The imperfective продавать would focus on the ongoing process of selling, like simply having it on the market.
Хотим comes from хотеть (to want). Why does it use an -им ending instead of an -ем ending?
Хотеть is a heavily irregular verb that mixes two conjugation patterns. In the singular (I, you, he/she), it uses first-conjugation endings and changes its stem to a ч (like я хочу, ты хочешь). But in the plural (we, you, they), it switches to second-conjugation endings and keeps the т (like мы хотим, вы хотите, они хотят).