How to refute this geometrical method to find MH370?
The picture says that "If [the above facts are] true, the plane can only be at one of two green dot locations." However, it doesn't give any reasoning or evidence to support this claim. So, there's no reason to think that the claim is correct.

You asked if itʼs possible to prove that the method is wrong. Itʼs not possible to prove that the method is wrong, because there is no method here. The picture is merely a collection of facts and unsupported claims.

However, the picture does seem to rely on a particular premise. Specifically, the picture seems to be based on the premise that the departure airport, the Inmarsat satellite, and the crash site must form a right triangle. That premise is false; the locations of airplane crashes are actually not affected by the positions of overhead satellites (or vice versa).