I have two servers: Data server A and client server B.
They are connected via a LAN switch and via my private switch.

Server A is an Oracle Data Appliance and has two IP addresses: 156.40.59.12 (not exact - A) and 192.168.2.3 (AB).

Server B runs a Red Hat variant and has two IP addresses:
156.40.59.13 (not exact - B) and 192.168.2.148 (BA).

I can ping Server A from Server B using either address and I can mount an exported filesystem from A on B, BUT I can't mount AA on BB because it says:

# mount -v -t nfs -o clientaddr=192.168.2.148 AB:/data /export/home/data
mount.nfs: timeout set for Tue Aug 16 14:26:05 2016
mount.nfs: trying text-based options 'clientaddr=192.168.2.148,vers=4,addr=192.168.2.3'
mount.nfs: mount(2): No route to host
mount.nfs: trying text-based options 'clientaddr=192.168.2.148,vers=4,addr=192.168.2.3'
mount.nfs: mount(2): No route to host

Any suggestions?

Roger

Check your firewalls

post results of ip route show from both servers.

I only know how to show the one route - the other is a data appliance. No cmd shell.

156.40.59.128/26 dev enp16s0f0 proto kernel scope link src 156.40.59.13 metric 100
192.168.2.0/24 dev enp129s0f0 proto kernel scope link src 192.168.2.148 metric 100

Have you done what I had suggested?

It is supposed to show ALL the routes the kernel knows about.
Please share with us the results of the command and we will be able to move from there.

Yes, I ran the command you suggested and posted the results for the Red Hat client server. I can't do that for the Data Appliance because it is menu drive; there is no access to a command shell.