I'm guessing the these are 1/4" backs with an extra 1/4" or 3/8" glued on horizontals at the top and bottom of the backs. The sides are likely 1/2" material - plywood? - particle board? and these are slotted to receive the 1/4" backs which are likely just siliconed in place (maybe a few added staples). Fully loaded with dinner ware, these type of cabinets could fall off the wall regardless of how many studs the backs are attached to because the weight of the load could simply pull the cabinet(s) apart.
The question is what you intend to place in these cabinets. Even all ganged up (each box securely fastened to the other through the side walls and/or face frame) and hanging on a rail could utterly fail if they are secured through their flimsy backs - thus the need for a bottom support or soffit. Having two cabinets that rest on the counter top and flanking the attached center section of cabinets is a good solution too. Also useful if the cabinets are set and secured between two walls, with a stud or two to catch the front edges of the cabinets. A sidewall of a refrigerator cabinet can serve the same purpose if the cabinet can be through bolted to it.
In my work I will gang up runs of wall cabinetry to 60" regularly, but my cabinetry is 3/4" ply with glued and screwed 1/2" backs. The system of ganged up boxes like this can easily be supported by 4 studs using 3" # 9 washer head screws top and bottom through the back of the cabinets. If the the stud layout is not favorable, it is useful to remove the sheet rock behind the cabinetry and apply 1/2" plywood directly to the studs or letting in some 2x6 blocking.
Hanging rails is always a nice solution if the finished sides (visible sides and bottom) of the hanging cabinets are not spaced off the wall requiring some kind of trim detail. I wish that manufacturers provide load ratings for their wall cabinets. That would tell you more than width and height.