MPLS Layer 3 VPN communication between CE routers
Specifically, communication between the networks on the Fa0/0 interfaces is not possible. This is because these networks are not advertised to the remote CE router.
If you issue the following command from CE1:
CE1 will send an echo request to the L0 interface of CE2 using the IP address of Fa0/1 as the source address. The ping will reach the L0 interface of CE2, but will not return because CE2 does not have the 192.168.12.0/24 network in its routing table. Similarly, CE1 does not have the 192.168.45.0/24 subnet in its routing table.
These routes are not needed to make MPLS Layer 3 VPNs work!
In order to correctly verify MPLS Layer 3 VPN connectivity, the source of the ping should be the local loopback, like so:
ping 126.96.36.199 source loopback 0