From the fourth quarter onward, can we see the moon in the afternoon sky?
At third quarter the moon rises at about midnight and sets at about midday The exact rising times depends on the position of the moon relative to the ecliptic and the season.
So in spring, at third quarter, the moon is low and sets quite early (around 10:00 in my location) In Autumn the moon is high at third quarter, and sets at about 15:00 (though daylight saving time affects this)
As the month progresses the moon rises later and sets later. The moon is above the horizon in the afternoon, but visibility depends on many factors, and a very thin cresent, close to the sun, may not be visible with the naked eye. There is some analysis of this with respect to the appearance of the new moon, (which has calendrical significance to some religions) There are too many uncertainties in determining visibility to give a simple answer, much depends on the observer.