Should be fairly easy with some transparent corrugated plastic roof sheets. Make sure it is closed all around to prevent high winds from lifting it off, but also have sufficient windows for ventilation in the summer.
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Very cool project! I have a couple questions:
Do you get snow in your area? If it sheds from the house roof that could be an issue.
What is the siding on the house? Greenhouses can get pretty humid/damp so you'll probably want to ensure it doesn't/can't rot the house. It can still be done but it's good to plan for. If your house is concrete that would be much less of an issue.
Also what's the directional orientation of the 12x24' space? You'll probably want to optimize your layout for sun exposure, so it'll help to know what parts will be shaded when (such as by the garage) and where the sunlight will track.
No snow.
Siding is stucco, so I'm not worried about wood rot
House is on the north, garage is on the south, the 24' is along the E-W line, so the sun should track right over the breezeway
Sounds like a great location! I'm in a very different climate zone so most of my advice would have been around keeping the temperature warm enough through winter, while it sounds like you won't have to deal with a lot of that.
I've seen some cool designs that made glass houses out of secondhand windows or slider doors - if that appeals I can share some links but it's a certain kind of look, and Povoq's suggestion of clear corrugated sheets is probably easier and more uniform. Rain collection from the house roof and greenhouse roof would be very useful.
I'll see if I have any good links for you