Not all the available PCIe lanes in an Intel PC are available from the CPU. Some come from the PCH (Platform Controller Hub) AKA the chipset. The PCH communicates to the CPU over DMI, which itself is usually connected to via 4x PCIe lanes. All devices on the PCH share that bandwidth, so typically things like GPUs, RAID cards, and other devices aren't made with this in mind. But all the ancillary devices in the computer hook up to this, SATA controllers, onboard lan, some NVMe drives.
Higher performance devices get hooked up directly to the CPUs available lanes.
Motherboard manufacturers have these lanes to allocate through switching or simple direct connection.
What they are telling you with those numbers is the configuration of the lanes and slots. 3x PCIe 3.0 is basically saying you have 3 PCIe slots that are hooked up to the CPU, available modes are 16x/16x/16x or anything less. (Though that is slightly simplifying it a little) All the others, including one x16 slot, is hooked up to PCIe 2.0 through the PCH (That should be an older motherboard, does anyone know if AMD uses PCIe 2.0 on threadripper?) Intel has in the past, but not on their recent stuff (I think)
Typical Intel consumer, Z class CPU, 16x PCIe 3.0, supported modes are a single 16x card (16x/0x). Two 8x cards (8x/8x) and occasionally (8x/4x/4x) for three cards. All the 1x slots and usually one x16 slot (at only 8x mode usually) run through the PCH.
28 Lane CPUs behave differently than 44 Lane CPUs in X99 and X299 boards. So the possible configurations get more complicated. Suffice to say, typical 28 Lane CPU can handle 16x/0x, 16x/8x/0x , 16x/8x/4x.
44 Lane CPUs 16x/16x/8x, 16x/8x/8x/8x, 8x/8x/8x/8x
If there is any room after that, then the smaller slots will still be running off the PCH.
It has been brought up before, but there are boards that support larger configurations using full PCIe bridge controllers (same ones found in the old dual GPUs), but in name only. They are still limited by the bandwidth available to the CPU.
I suggest posting your final build for a once over by others to make sure you get what you are after.