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Ok, this sounds a lot like part of my project but I'm using an 8 space load panel where I'm using a 20 space panel... And using smaller cable, I'll get to that.

First of all, it looks like you've probably got Square D Homeline? Just wanted to check because they have 2 lines, one is Homeline and the other is QO. I'm using a Homeline panel so if that's what you have then I can refer to my own stuff. Also, I saw they have 8 space main lug and main breaker, this needs to be main breaker so you have a main shutoff in the garage.

Your original question is a little unclear if you're asking about the connections at the house end or the garage end, it sounds like you are asking about the garage end, but it also sounds like you need guidance for both ends.

First, it sounds to me like you have black and black with gray stripe which should be your two hot conductors. White should be neutral. Green should be ground.

On the top of the main breaker there are lugs for each hot on the outside. In the center is the lug for attaching the white neutral wire. 2 bus bars should be near the sides of the panel and one should have a lug on it for attaching your ground.

On the other end of your cable in the house, your green ground again attaches to the ground bus bar and the white attaches to the neutral bus bar. You might have to get larger lugs that attach to the bus bar because 2 gage might be too big for the screws in the bus bar. Your black and black with gray stripe hots go into the 2-pole breaker on your panel.

2 gage aluminum is not big enough for 100 amps. You can use the 100 amp panel, but the breaker in your house will have to be 90 amps or smaller. At 120 feet you might have voltage drop issues which might require the breaker to be smaller, my garage is only 30 feet from the house and I don't have to factor that in... Somebody else would have to speak to that. Table 310.16 applies and your probably going to need the 75 degree column...

I'm assuming you have a permit and there will be inspection, folks tend to be more comfortable answering questions when that is acknowledged.
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