Identify the phases of the moon if at sunrise the moon is near the zenith, near the western horizon, and at sunset in the south-western sky.?

If the moon is near zenith at sunrise, then it rose at midnight, making it the last quarter.
If the moon is on the western horizon at sunrise, then it's setting, making it full moon.
If the moon is in the southwestern sky at sun set, then it's a waxing crescent.

Last quarter (roughly)
Full Moon (roughly)
New moon - and your sentence is confusingly constructed.