If a nearby neighbor can get 6 over-the-air (OTA) channels and you have a good outside antenna, you should be able to get the same channels, no question. The first thing to do is determine the health of your outside antenna. It could be quite old, with corroded connections where the downlead (coaxial cable) connects to the antenna. The downlead itself may have deteriorated due to weather. It may take some work, maybe some professional help, but a good antenna and downlead are essential to OTA reception.
Before going to all that trouble, though, check the basics of your converter and TV. The easiest way to connect the converter to your TV is via composite cables (yellow-red-white) if the TV has a matching set of auxiliary input jacks. You just select that input with the TV's remote.
Failing that, connect the converter's coaxial output to your TV's antenna jack. The converter most likely came with its output channel set to analog ch. 3. It could also be ch. 4. Whichever it is, put your analog TV on the same channel (3 or 4) and leave it there permanently. You change channels with the converter remote, not the TV remote.
Next, scan for channels. The user guide for the converter will tell you how. It will most likely be a menu function. You will have to rescan any time you make any adjustment to your antenna for the purpose of receiving new channels.
You should get solid reception on those 6 channels, and somewhere in this answer is what you need in order to do it. Good luck.