Which type of hybridization leads to a trigonal planar electron domain geometry? s sp sp2 sp3

Electron domain geometry takes into account the bonds and the free electrons around the atom to predict the geometry.

A tigonal planar geometry means that all the electron domains are in the plane and that they are as far away as they can. That means that there are three electron domains in the plane separated at 120 ° each other.

sp2 means that there are three hybrid electron domains, and the geometrh that leads to the minimal repulsion force is they placed at 120°, which exactly the trigonal planar geometry described up.

Then the answer is sp2

You can check in your book, that sp corresponds to two domains, located linearly, at 180°; and sp3 is four domains with the form of tetrahedral with 109.5° angles.     

There are no metaphors.