how many orbitals in an atom can have for the following designation?

4px, 4dy, 4dz, 3dx, 3dy, 3dz, 3dz2, 6dx^2-y^2

I can do basic problems such as 3p=3, 3d=5, ect......but I really don't know how to figure it these designation. Can you please explain more to me? Thank you for your help!

if it is 4px --- it is only one orbital means 4p orbital on x axis
there are  no  orbitals with 4dy, 4dz, 3dx designation
3dz2, -- one such orbital
6dx^2-y^2  -- one such orbital

if it is 4px --- it is only one orbital means 4p orbital on x axis
3dz2, -- one such orbital
6dx^2-y^2  -- one such orbital

How do you know these have one orbital? I just want to know how to do other problems just like this. Thanks again!

4p has three suborbitals --- 4px ,4py and 4pz
so 4px is only one with n=2, l= 1 and m=-1
similarly you check for d orbitals
it has five suborbitals---- dxy .dyz,dxz , dx^2-y^2  d z^2