This can be hard to do when you're starting out and don't have experience with flash specs and what they do and don't say about wireless triggering capabilities.

Flash specs to look for

Looking over the Sunpak DU4000U, it's unusual in being a "universal" flash that isn't single-pin and manual for all ISO-compatible hotshoes. It's a flash that can be TTL for either Canon or Nikon, and it has an unusual pin pattern that covers both hotshoe contact layouts in one foot.

Single-pin vs. TTL

If a 3rd-party flash is single-pin, that is, only has the sync pin on its foot, like the Yongnuo YN-560 IV or Godox TT600 that means it cannot do TTL/HSS on a flash hotshoe and doesn't do full camera/flash communication through a hotshoe. Add-on triggers to the foot of the flash or corded to a syncport can only fire these flashes, and with radio, you always need a transmitter on the camera and a receiver in or attached to the flash. And with a single-pin flash, you'll only get more than firing the flash if it has a built-in radio trigger and you use a transmitter that's in the same radio communication system (not just the same brand; same brand and system).

How to tell if your flash as radio remote control

You can tell if a flash has built-in radio because the radio frequency will be in the specs: typically 2.4 GHz or 433 MHz. But you need to look for more than a matching bandwidth to have a compatible transmitter. It's like how wi-fi and bluetooth both operate on 2.4 GHz, but use different communication protocols. The protocol also has to match.

Your DU400U, however, has no radio frequency spec on it, so it has no built-in radio. So, radio triggers like the Flashpoint R2 SPT and Yongnuo YN-622C/N triggers would never work without a second unit to act as the receiver on the flash (attached to its foot) as well as one to act as a transmitter on the camera.

And whether you would get TTL or HSS or not over radio would depend on whether the camera, flash, and triggers can do these features as well. Trigger-wise the Yongnuo YN-622-TX/YN-622 or Godox X1R/X transmitter combos can; the Flashpoint R2 SPT or Yongnuo RF-603 II cannot. But this type of communication is brand-dedicated. So if you have a Canon camera, you need Canon-compatible gear; if you have a Nikon camera, you need Nikon-compatible gear.

Smart optical control

However, from the specs [wireless control: eTTL/iTTL], and the fact that you have Group and Channel settings (indicators you've got TTL/HSS wireless communication of some kind, but both are used for radio and smart optical communication) indicates that your DF400U does have "smart" optical wireless built-in. This is a light-based wireless communication system, kind of like using a tv remote.

Canon's is called wireless eTTL; Nikon's is called CLS/AWL. To use this feature, some cameras have pop-up flashes with master/commander capability to remotely control the flash. But if your camera is too low-end or doesn't have a pop-up flash, then you need a flash unit on the hotshoe that can be the master/commander (e.g., a high-end speedlight, or a dedicated optical transmitter). For a Canon shooter, something like a 580EX II speedlite or the ST-E2; for a Nikon shooter, an SB-900 or an SU-800. Or a third-party speedlight with this function (e.g., the Godox Mark I TT685-C/N V860 II-C/N speedlights).

So, the ST-E2 can remotely trigger a DU400U, but it's a very old controller with limited power/group control. You have no M power control, it can only do two groups (A:B) as TTL power ratios. But you can get HSS with it. And it will only work if you're a Canon shooter.

The drawbacks of using optical vs. radio are that ambient light levels can affect the range and reliability and you need line-of-sight between the sensor on the flash and the master/commander unit on the camera. Optical systems work great in studio conditions (lower ambient, lots of bounce surfaces), but can be more of a PITA when used outside in bright sunlight.

Dumb optical S1/S2

In addition to this, the DU4000U also has S1/S2 "dumb" optical slave modes which are simple sensors that fire the flash when another flash burst is sensed. You can use any flash burst (except LED "flashes" on phone cameras) to fire the flash. But all you can do is fire the flash. There's no remote power or group control, TTL, or HSS.

S1 fires the fash on the first burst sensed, S2 on the second burst sensed, so the "master" signal can use TTL and the off-camera flash won't fire too early on the metering pre-burst. Additional pre-bursts, like those used to transmitter "smart" optical settings or for red-eye reduction, can throw off the timing on this so the flash doesn't fire in sync with the exposure.

So your answer here if you don't want to get more than one trigger, is to use a "smart" optical commander/master unit, or a pop-up flash and the S1/S2 modes.