How many phases are in a homogeneous mixture?
A homogeneous mixture implies the phases are homogeneous. We generally refer to these as solutions.
Hence, there is one phase in an ideal homogeneous mixture. For instance, the air you breathe and the water (spoiler, it's not 100% pure) you drink are solutions.
Homogeneous mixtures exhibit no physical boundary between the components, so they present as a single homogenous phase.
Examples are things such as salt dissolved in water, sugar dissolved in water, or various polymers dissolved in solvents.
This is distinct from heterogeneous mixtures where there there is a distinct surface or boundary between the components. For example, dispersion of clay in water, where there are solid surfaces of the small clay particles, or oil in water emulsion, where the oil and water are immiscible at the molecular level.