I have given the triangulation in black:
The task is to refine the two triangles on the top (left) in 4 congruent triangles each. I have done this in red colour.
In addition to that, there should not be any hanging nodes. I tried this using the violet colour. Is this correct, or is there any fault?
Thanks in advance for checking my draft.
Corrected version:
This is it maybe if I figured out your question correctly.