Hey this is a bad question because we do not know if the rings are distinct and fingers are distinct.

For example if all the rings are same but fingers are not then the problem is to arrange 6 things in 4 places.

Let the rings in each fingers be x1, x2 .... x4.

So essentially you are asking how many solution to the equation

\(x1 + x2 + x3 + x4 =6\)

The number of different ways to distribute 6 indistinguishable rings into 4 distinguishable fingers is C(6+4-1,4-1).

or C(9,3)=\(\frac{9!}{3!6!}\)=84