ssh not connecting

I'm not able to connect to my computer through ssh. Here are the steps I've taken already:

1. Linux (Ubuntu) connected to internet--check
2. Ran sudo apt-get install openssh-server (on the receiving machine)
3. Ran sudo apt-get install openssh-client (on both the receiving and remote machines)
4. Ran sudo service ssh status to verify server listening on port 22--check
5. Ran sudo ufw status to check firewall, return status: inactive
6. Got the IPv4 and IPv6 addresses
7. From my remote machine, attempting to log into the server, I use: user@hostipaddress (where "user" is the username on the server, and "hostipaddress" is IPv4 or IPv6 address)

Results: When I use the IPv4 no connection is made and I get a timed out error. When I use the IPv6 from home (same, local wireless network) I get access and I am prompted for my password (all is good). However, if I use IPv6 from a remote network, I get a "Network is unreachable" error.

I'm fairly new to Linux and command lines, so I'm not sure what I'm doing wrong. Thoughts? Suggestions?