To begin, there is no such thing as "triple channel ram". You can have ram run in different configurations: single channel, dual channel, triple channel, and quad channel. The possible configurations are dictated by what the motherboard is made to support (as well as what the cpu is made to support). Your motherboard can run ram in single, dual, and triple. Here is a little video that explains what I said about channel configurations:
https://www.youtube.com/watch?v=-D8fhsXqq4o
In theory, dual channel is better than single channel and triple is better than dual. However, this doesn't not translate to much tangible real-world performance gains, if at all. This would mean that you can just run a single module of 16GB of ram and not notice any difference than if you had 2 8GB modules running in dual channel. Here are some links that show tests and benchmarks that demonstrate this:
http://www.pcworld.com/article/2982965/components/quad-channel-ram-vs-dual-channel-ram-the-shocking-truth-about-their-performance.html
http://www.overclock.net/t/681697/the-truth-about-i7-1366-memory-both-dual-channel-vs-tri-channel
If you want to upgrade from 6GB to 16GB, you would want to focus on finding matching ram. For ram to "match", they need to have the same rated speeds, , size, rated voltage, and timings/latencies. It is also very important that the actual chips on the PCB matches. Sometimes manufacturers may decide change out the chips they use for a particular lineup of ram due to costs or supply limitations, leading to 2 packages of ram with the same product ID not working together properly in rare occasions. This may not always be the case, as sometimes mix and matched modules of ram CAN work together perfectly.
In this case, you can simply buy 2 packages of 2x4GB ram, 1 package of 2x8GB ram, or just 1 module of 16GB ram. As long as they packages are of the same product ID, you can feel fairly confident that they could match. Just run Memtest once you installed them to check if you actually are working well together.