By default Cisco ASA design does not allow traffic to flow between two interfaces having the same security level not sourced and destined on the same interface. To ‘fix’ this issues there are two commands you can use.
Configuration example:
ASA# conf t ASA(config)# same-security-traffic permit ? configure mode commands/options: inter-interface Permit communication between different interfaces with the same security level intra-interface Permit communication between peers connected to the same interface ! ASA(config)# same-security-traffic permit inter-interface ASA(config)# same-security-traffic permit intra-interface ! ASA(config)# end ASA# wr mem