So I assume you are getting the ASRock Z77 Pro4 motherboard. The Arctic Alpine 12 cpu fan cooler includes a 4-pin PWM fan, so that should plug into the mobo CPU_FAN1 header with 4 pins, and ignore the CPU_FAN2.
The Riotoro CR400 case comes with two fans. It appears that the front one in a red LED fan, but the rear one may have no lights in it. Use a Splitter to connect these to the appropriate mobo header. If they have 3-pin connectors, use the 3-pom CHA_FAN2 header; if they have 4-pin connectors, use the CHA_FAN1 header. In either case, get a Splitter like this
https://www.amazon.com/Splitter-Com...ords=4-pin+fan+splitter&qid=1618261762&sr=8-5
That's a 2-pack of 4-pin Splitters with three output arms each. You only need one. The third arm is just in case you decide later to add a second front fan. Even with 3-pin fans you can use this Splitter. And irrespective of the 4-pin design of the Splitter, you plug its female into the mobo header for the type of FAN you have: 3-pin or 4-pin.
Note this is NOT a fan HUB. A Splitter has only two types of "arms": one female input arm to plug into the mobo header, and two or more male outputs with pins. A mob header can deal with the speed signal sent back to it form only one fan. So a Splitter will only send back the speed of ONE of its outputs, and ignore the rest. It does that by the pins in the outputs. Note on them that only ONE output has all four pins, and the others are missing Pin #3. So you MUST plug one fan into the output with all four pins, and additional fans into the others. Your mobo will only "see" that one fan's speed, but this has NO impact on ability to control all their speeds. A HUB has an additional "arm" that must plug into a power output from the PSU, and it can work only with a 4-pin header AND 4-pin fans, so don't get one.
The limit in using a Splitter is that almost all fan headers can supply up to 1.0 A total current max to all its connected load. Most fans today draw 0.10 to 0.25 A max per fan. So three of those can easily be connected to one header. A LED fan with added lights has a higher current, as much as 0.45 A. But still, ONE of those with a couple of fans at 0.25 A or less each comes in under 1.0 A total. The case web page does not give those fan specs, but you can check them from their labels when they arrive.
That takes care of the CPU cooler and case ventilation fans. Just a couple other note FYI. A lot of PSU's now come with modular cables. That is, most or all the cables are NOT wired inside the PSU. They all plug into distinctive sockets on the PSU exterior. But they are NOT universal, so use ONLY the cables that come with your PSU. For the most part they are well labelled so little confusion. Cab;es for add-on devices sometimes are not so clear. The older IDE type of HDD's and many optical drives use a power input called 4-pin Molex. The cable from the PSU has a female (with 4 holes in ones straight line), and the socket on the rear of the drive is male with 4 pins. This power connector has become widely used for lots of things. The newer SATA drive units use a different connector for power. But more generally, both types of drives (and other devices) are Peripheral Devices, so many cables are labelled for "Perif", and do not say "Molex" or "Sata". It is common for a PSU to include two or three identical cables for Peripherals. On each cable set there may be several SATA AND several 4-pin Molex output connectors. On at least one there will be a much smaller 4-pin female connector that looks a LITTLE like a fan connector. But that really is the power input for an older 3½" FLOPPY drive unit if you have one. Don't try to use it for anything else.
OP, for you and Vic40 above, about the PWR_FAN header (item 37 in the diagram on manual p. 13). You won't have a use for this, because your PSU will not have a wire set for it. 20 years ago or so this was a feature. It looks like a standard 3-pin fan header but is not. Its intended purpose is ONLY so you can plug into it those special wires from a PSU with this feature. All it does is accept the speed signal coming from the fan inside the PSU, so your mobo can show that to you. It does NOT actually control the speed of that PSU fan - any such control is done solely by the PSU as an internal function. However, SOME mobo makers also provided the +12 VDC (pin #2) and Ground (Pin #1) supplies to that PWR_FAN header, even though it could not alter the voltage on Pin #2 as a normal fan header does. That way it could be used as a power output, but ONLY for a fixed +12 VDC supply with no "speed control". So it is best left unused when your PSU does not have that set of speed signal output wires.