I had installed an SQL Data Engine and a Microsoft SQL Server Management Studio on my other computer, the catch was that I wanted to able to connect to the data engine installed on the other computer. I followed the tutorial listed here and also watched several YouTube Videos to help me connect to an SQL Data engine on another computer through the internet. All the hours I spent, no luck at all.  After trying to connect several times and then failure after failure, I watched one YouTube Video Here and then realized that, after port forwarding on SQL Configuration Manager and  Firewall configuration  I had to put the computer IP Address (Remember: Computer IP address changes when you connect to the Internet with Ethernet or through wireless. Make sure you check what IP address the laptop is using at the moment: The idea is to use the right IP address so the Router directs the traffic to the right computer on a specified port) in format like this; 197.164.1.46,portNumber (e.g. if port number you specified is 4356 then 197.164.1.46,4356  in SSMS Logging Server Name Field, then put your user and password) you specified in SQL Configuration Manager if you follow the tutorial. Done!! Wrote By: Ernest Mushinge                      03/25/18