there is many types of support to be used for counter top for long lasting work... as ... 1) brick wall which takes 2" , 4" or 6" thickness space which is not good for below space as we will waste space for storage under counter... this is used where heavy material is used on top of counter for cutting any food items... 2) marble support... which will take 35mm thk space double support... 3) furniture base if the kitchen working person is using the sink properly for washing purpose and the gaps between the sink and counter top has to be sealed properly for leakage free to avoid any damages for below storage, as i will not prefer this in other area... this can be used only in foreign countries...

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Your quartz should be installed on a level surface. But there are a couple of ways to make this happen. For one, you may be able to place shims under the cabinets to level the tops. Or, you might opt to put plywood over the cabinets placing shims underneath the plywood as needed. Greetings from Aura

In that case , wall hung cabinet would be able to support the slab and sink. Is there a reason you want it it to be wall hung cabinet. You have made safe skirting space and even a floor mounted cabinet should be fine here. Regarding material, for the carcass you can opt for granite vertical slabs and BWP ply shutters for floor mounted one. But if you prefer a wall hung cabinet then a BWP ply carcass sould be good enough. The wall groove should be cut only on the longer side. Thanks, Nitin Cornerstone Designs, Bangalore