How many fases of the moon is their?

First of all , to correct your English spelling. It is 'phases' , NOT 'fases'.

There are four phases. They are ;-

New Moon

(Waxing Crescent)

First Quarter

(Waxing Gibbous)

Full Moon

(Waning Gibbous)

Last ( or third ) Quarter.

(Waning Crescent)

Next New Moon

The bracketed terms are the visible shape of the Moon between each phase.