Wiring from basement main panel to garage
You are using individual wires, so you need conduit all the way if you don't want a box

Since you are using individual 4AWG THHN wires (instead of some sort of cable), you will need to run in conduit all the way from one panel to the other, unless you wish to have a box somewhere inside the house where you transition from the conduit wiring method to some flavor of cable (SER or NM).

A continuous conduit run inside can be practical, though, depending on what you are running through; the key here is to remember to provide ample pull points using LL and LR conduit bodies instead of bends whenever possible.