You must have a DL160 'Generation 6' as the G5 didn't support the E5506.
The supplier is wrong, the G6 supports 18 memory slots, each capable of taking a 16GB DIMM for a total of 288GB.
The way that modern Xeon's work is that they have THREE memory channels per CPU, with each memory channel for this model having 3 DIMM slots per channel - totalling 9 slots per CPU so 18 for the machine.
If you only have a single CPU you shouldn't fill out any of that CPUs 9 memory slots but for optimum performance you should use fill out all three memory channels per CPU evenly. So where dual-channel systems (such as older systems and desktops/laptops) would go up in 1GB/2GB/4GB/8GB/16GB/32GB increments with the new three channel system you go up in units of 3, so 3GB (3x1GB), 6GB (3x2GB), 12GB (3x4GB), 24GB (3x8GB) and 48GB (3x16GB) PER CPU. Then when you memory slots are filled out that way you can then use the second per-channel memory slot, again ensuring that they're filled out uniformly.
Now you can use just two slots per channel - as the memory has been shipped in your case - but I wouldn't suggest it - you'll be losing out on performance.
You don't mention how many CPUs you have but if you have 2 x 2GB already and have only a single CPU then I'd suggest you buy FOUR more of those 2GB modules for a total of 12GB or SEVEN extra for a total of 18GB. If you have dual CPUs then I'd suggest you either buy FOUR for a total of 12GB or TEN for a total of 24GB - anything else is a needless compromise.
Hope this helps.