How can one able to understand Half beats, Atiit and Anagaar... (Like here, the artist tries to explain it, but I am unable to get it)

Perhaps a session on Taal can include tips on how to pick up at half beats. Many of Dr. Ashwini Bhide's compositions start at half beats and are really difficult for students to learn.

Try following the theka in the video by counting the beats first. This is a 9-beat tala called Matta tala (or a variation of it), and its bols are "dhin tirakita dhin na, tin na dhin dhin na", and it will be a bit difficult at first. It is Jhaptaal, with the first five beats (dhin na dhin dhin na) replaced with the four beats (dhin tirakita dhin na). First try to get a feel for how he lands exactly on the sama (the first beat). When you get the hang of it you will be able to see how he lands on half a beat after the sama (in Ateet) and half a beat before the sama (in Anaghat).