Hey @robert-george that is a great question, let's see if I can help with this,
In the context of the question, the PCs in question are older so they are most likely running Fast Ethernet (100BASE-T) and to connect these two computers together would require a point-to-point connection since no switch is available or you could just simply connect both PC network adapters to the switch. Before we talk about wiring schemes it is important to understand what the pins in the network adapter do using the Fast Ethernet (100BASE-T) standard:
Network Adapter
1 - Transmit
2 - Transmit
3 - Receive
4 - Not used
5 - Not used
6 - Receive
7 - Not used
8 - Not used
These pins are physically mounted to the network jack and cannot be changed, however we can change how the Cat cable (copper-based Ethernet cable) is wired into the RJ-45 jack. When connecting to a switch we use what is called a straight-through cable which has the same wiring scheme on each end of the cable. When the switch receives a transmission into one of it's ports it does so on pin 1 and 2, then forwards the transmission to the destination PC on the receive wires in the straight-through cable, which is then in turn received on destination PC pins 3 and 6. The switch handles the "crossing-over" of the transmit and receive pins between source and destination PC. But we do not have a switch to do the "crossing over" for us so what do we do two crossover pins 1 and 2(transmitting) on the destination PC to pins 3 & 6 (receive) on the destination PC? We do that by manually wiring the cable so that on one end wires will match the transmit pins but on the other end of the cable we take those same wires and wire them to the receive pins (3 & 6) on the other side of the cable. This is accomplished by using to different wiring schemes on each end of the cable. What the heck is a wiring scheme? This defines how that wires are arranged into the back of the RJ-45 jack. There are two standards that we follow standardized by a group called TIA/EIA...568A and 568B. Here is what that looks like:
Network Adapter 568A
1 - Transmit >>>>>> White/Green
2 - Transmit >>>>>> Solid Green
3 - Receive >>>>>> White/Orange
4 - Not used >>>>>> Solid Blue
5 - Not used >>>>>> White/Blue
6 - Receive >>>>>> Solid Orange
7 - Not used >>>>>> White/Brown
8 - Not used >>>>>> Solid Brown
Note the color of pins 1 & 2 as well as 3 & 6
Now we will wire the other side of the cable with 586 B
Network Adapter 568B
1 - Transmit >>>>>> White/Orange
2 - Transmit >>>>>> Solid Orange
3 - Receive >>>>>> White/Green
4 - Not used >>>>>> Solid Blue
5 - Not used >>>>>> White/Blue
6 - Receive >>>>>> Solid Green
7 - Not used >>>>>> White/Brown
8 - Not used >>>>>> Solid Brown
Here is another view:
This will create that point-to-point connection that "crosses over" the transmit pins of one network adapter to the receive pins of another network adapter. I hope this helps and if you have additional question please do not hesitate to ask.
