Can someone explain the second point in the picture how n plane divides the space into 2 power n hash buckets?
Thank you
Hi Naveen_Malla,
This results from the Johnson-Lindenstrauss lemma, as explained here. You can find a formal proof of this lemma here.
Hard to put into plain English 
In reality the second point is not entirely true:
https://www.themathdoctors.org/cutting-up-space-using-n-planes/
I think it is used just for simplicity to approximate the number of hash buckets.