The garage is on a 4ft poured foundation-a typo? "Four inch," perhaps?
I am not a P.E., not a G.C., nor a structural engineer.
You could use a 2 x 4 at the bottom of the 2 x 12 for your mezzanine floor joists to rest-upon, or are you going to use some Simpson strong-tie U-shaped saddles for the floor joists? That would eliminate the need for the 2 x 4, and you could reduce the ledger board to a 2 x 10" and still provide room for the Simpson U-brackets, unless the 2 x 10" doesn't provide enough distance from the fasteners of the brackets, to the edge of the ledger, then you would need a 2 x 12" ledger.
I think I would use at-least 5" length fasteners for anchoring the (let's call it) 2 x 10 ledger board to the wall 2 x 6" studs. The thickness of the ledger, 1-5/8" plus 5/8" type X drywall = 2-1/4" thickness, and that would give you 2-3/4" screw penetration into the 2 x 6" wall studs. You might consider 6" long screws, then you would have 3-3/4" penetration into the wall studs. I would suggest a minimum of three fasteners per wall stud/ledger, top and bottom a minimum of 2" from the ledger edge.
As for the triple 2 x 6" end of the LVL beam connection, some type of flat steel gusset plate, through-bolted to the 2 x 6's and to the LVL with two 1/2" steel bolts per structural member should take care of that. I expect you would want to do something similar to the opposite end in-between the garage doors. A pair of similar angle brackets for the foot of the 2 x 6 column, on opposite sides, and tamp-in threaded pins or epoxied threaded pins should be used.
Is the OH door a gable end? That means the side wall of the mezzanine is going to be a lower roofline than going towards the middle of the garage, the long side dimension of the loft. Are you going to have any rail or protection from stepping-off the elevated floor of the mezzanine? Also, what is to be your access to the mezzanine? Do you have room for stairs, were you going to use a fold-down attic ladder (which would eat-up considerable floor space), or are you going to use an A-frame ladder, because it will be an infrequently-used/accessed space?
I put in a mezzanine in the back-half of my 2-car garage and have about 240 sq. ft. of storage. I put a jib crane up there, hanging over the edge, to allow me to safely move heavy objects up/down. That worked better than an I-beam and trolley at the ridge beam which would have significantly cut-down on the headroom in the mezzanine.
It's always good to have a P.E. review your design to ensure that it will meet the static/dead loads you may introduce there. Yes, it costs $ but you have an expectation of safety and durability/suitability for your intended use.
