full duplex vs half duplex is not the cause / solution to collisions on a network. That is mostly caused by a hub vs a switch. Hubs function as repeaters, every packet of data that a port receives, is sent out every other port. This creates a lot of unnecessary traffic. On a switch, there is a MAC address table and every packet is routed to the port that has the destination MAC address connected and only to that port. Collisions occur when two devices are sending simultaneously and their transmissions "collide" causing a spike in voltage and the data is then destroyed. TCP/IP protocols handle this event by detecting the increased voltage and basically doing a reset(i'll not go into the specifics of how this happens, but it does). The reason a hub can cause this to happen and switches are almost immune to the problem is simple. Imagine you have a 4 port hub, if two devices transmit at the same time, bam, collision. If you replace that hub with a switch, assuming the two sending devices are sending to different recipients, the switch is smart enough to basically route the data to the correct port. Its almost like having a traffic light instead of an uncontrolled intersection. In an example with a 4 port hub, this doesn't really present a problem, but as you grow to a larger and larger hub with more and more connections, the problem grows exponentially and happens more and more frequently. Switches on the other hand, just keep on sending data only to one port or the other.
Back to duplex, assuming an ethernet connection, half duplex vs full duplex will NEVER cause a collision because transmit and receive are on seperate wires. The real difference between half and full duplex are bandwith. Full duplex is effectively double the bandwith of a half duplex connection. 100mbps half, can send, or receive at 100mbps max. Full duplex can send AND receive at 100mbps in each direction at the same time without any delays, so effectively you have 200mbps of bandwith. What is useful about this is for troubleshooting purposes, if you have a slow network connection, one of the first things to check is the negotiated speed. If you have a gigabit network, you should see 1gbps as your connection speed(1gbps is always full duplex, 1gbps half duplex doesn't exist in ethernet specs) if you see 100/half, you know something is wrong. Either a bad cable, driver, or some other issue is preventing your connection from negotiating properly at the maximum supported speed.