Which is the best interpretation of the two flat portions of the graph?

In the two flat portions of the graph, the heat supplied does not lead to rise in temperature.

Latent heat is the heat supplied to a body which does not result in a rise in temperature. The word "latent" connotes "hidden".

Thus, at those two portions of the graph, the heat supplied leads to the breaking of the intermolecular bonds of:

Hence, those portions are flat because, the heat supplied does not result in rise in temperature.

For more explanation on latent heat see:

a) the particles of the chair are strongly held together.