Learn Russian: Завтра у нас переезд, и мы тащим мебель в грузовой лифт. - Tomorrow we have a move, and we are dragging the furniture into the freight elevator.

Even though moving furniture might involve multiple trips back and forth, the speaker is focusing on the specific, continuous action happening in one direction: from the apartment into the elevator. The verb тащить emphasizes the heavy, single-direction effort of pulling these items to their immediate destination.

The sentence starts with Завтра (tomorrow), but тащим is in the present tense. Why?

Just like in English (Tomorrow we are dragging...), Russian often uses the present tense to describe a firm plan or scheduled event in the near future. Because the speaker is vividly describing an ongoing, planned process, the imperfective present тащим works perfectly here instead of a future tense.

Why say у нас переезд instead of using a verb like мы переезжаем (we are moving)?

Both are grammatically correct, but using у нас (we have) with the noun переезд (a move or relocation) is a very common, natural way to frame a scheduled event. It treats the move as an upcoming appointment, exactly like saying у нас экзамен (we have an exam) or у нас собрание (we have a meeting).

Why is it в грузовой лифт (Accusative case) rather than в грузовом лифте (Prepositional case)?

Because this is an action directed into a new destination. The Accusative case after the preposition в indicates the direction of motion (into the freight elevator). If you used the Prepositional case (в грузовом лифте), it would mean you were already locked inside the elevator, dragging the furniture around within that confined space!