How to plug into Mac Air a 4pin Microphone with 4pin headphones through a splitter?
You are probably correct in assuming you need a 2x4 pin(f) -&gt; 4 pin(m) adaptor. You have an adaptor that splits for a headphone and microphone. What you need is an adaptor that splits for two headsets. In other words, everything (headphone, microphone and Mac) is TRRS.
I was able to find TRRS Y adaptor/cables for purchase by searching Google for TRRS Male to Dual TRRS Female. For example, this was the first link I encountered. The excerpt below was taken from this link. This excerpt actually states for use with 4 pin mini jack microphones.

Plus, allow you to connect one headphone, and one external 4-POLE TRRS microphone (NOT 3-pole TRS microphone) to Laptop, Tablet, PC computer or Smartphone into the 4-POLE 3.5mm jack at the same time.

Be aware there are two standards in use for TRRS. Basically, the difference is the sleeve and adjacent ring are reversed. See the image below.

You may need a converter which switches the ground (common) with the microphone. An example of a converter is shown below..

The above adaptor can be found here.

Note: If a adaptor is needed, then the adaptor should be placed either between the headphone and the splitter or between the splitter and the Mac.