The colours show the order in which I constructed the graph. Every vertex must be part of one face of order 4, so I start with a square (black, centre).
Now, each vertex is of order 3, and the four vertices have order 2, so extend one edge out from each. They're next to their face of order 4, so these edges must be parts of hexagons (blue).
We now have four vertices which are already of order 3 and missing their face of order 4, and eight vertices which are of order 2 and missing their face of order 4. Create the suitable faces (red).
Now each "edge" of the square formed by the red edges is really three edges, and they must each form part of a hexagon. The 4 corners of the red square are order 2, so they need one more edge each, and that brings us to 5 of the 6 edges of each hexagon, so just join them up in the green square.
Check: the outside face is also of order 4, so this works.