The answer to your question will be determined by the hardware system you select to open the door. Find that and the specs will give you the spacing. As an alternate to the one you show, take a look at the one below we did for a recent client. This is Blum Aventos lift,which gets the door up and out of the way. We also did not do a cabinet bottom to the appliance area - just the continuous counter. This makes it easier to pull the toaster and coffee maker in and out.

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Post some pics but IMO appliance garages are just a PITA and eat up counter space they are a dated look but without seeing anything about the space how it would work is a mystery. In athe ones shown you still have to move the pieces to use them so really kind of useless .

I love my appliance garage. I have the one pictured in Edmond's post. You may want to check what your cabinet company offers. It seems each company has it's own offerings with dimensions.