I am a bit confused with the ospf type E2 route. As per the doc when a route is marked as type E2, it does not calculate the metric to the ASBR
Then referring to the attached diagram, why isn't that iam seeing 2 routes for the subnet 188.8.131.52/24 and the drfault 0.0.0.0
R2 and R4 have been configured with default-information originate command
At R3 I see only one default route from R2.
What you are seeing is called recursive-routing. In order for R3 to know about routes from R4, the cost is 2 from R3 (see show ip route)
O 184.108.40.206 [110/2] via 220.127.116.11
while in order for R3 to know about routes from R2, the cost is 1 - the cost of the fastethernet interface.
Increasing the cost on the fastethernet interface on R3 that is facing R2 (ip ospf cost 2) should provide the desired result.