12 earrings 

Assume that there are R rings, P pins and E pair of ear-
rings. 

It is given that, he has 2 1/2 times as many rings as pins. 
R = (5/2) * P or P = (2*R)/5 

And, the number of pairs of earrings is 4 less than the 
number of rings. 
E = R - 4 or R = E + 4 

Also, there are total 26 pieces. 
R + P + 2*E = 26 
R + (2*R)/5 + 2*E = 26 
5*R + 2*R + 10*E = 130 
7*R + 10*E = 130 
7*(E + 4) + 10*E = 130 
7*E + 28 + 10*E = 130 
17*E = 102 
E = 6 

Hence, there are 6 pairs of Ear-rings i.e. total 12 Ear-
rings