When upgrading from 4GB to 8GB the system beeps.

Are you using a matched pair or a mix and match set? Mix and matching modules can work, but they need to be the exact same spec, or really close with HP. Brand (usually) doesn’t matter on this generation, but the newer HPs (think EliteDesk/ProDesk, and some "consumer grade" machines on the Pavilion side) can be quite picky at times. The problem with mixing most OEM modules is most prebuilts use the cheapest modules junk they can get which boot, so you need to use equally cheap and nasty modules in many cases. Since the CL ratings are generally way off between any retail module worth selling and OEM (usually good enough for OEM, but failed for retail), it usually doesn’t work unless you get lucky. You generally need to find the exact same module or a similar module to make it work, and even then, it tends to have stability issues unless it’s a near perfect match. This is why we don’t do it in a professional setting - it takes way too long to make it work.

The other issue is HP hardware has historically been... questionable about this practice for years. In many cases, you genuinely need the matched kit with how picky their BIOSes can really get. HP is about as bad as Apple, but a little more forgiving then Apple.

What I would do is buy a 16GB 2X8GB kit from Crucial or Corsair and do a matched pair upgrade - this machine supports 16GB natively, so it isn’t a problem. Even if it didn’t, it doesn’t tend to be an issue as long as the PCH supports it and there is no artifical BIOS imposed limitation. It doesn’t cost much more to get a 16GB set, which will put you in a better position long term over installing 8GB. Having a 2 DIMM board puts you in a poor position since you can’t buy a 2X4GB kit now and get an exact match to what was installed later - if they even still sell it. The i3-6100 technically supports 64GB, but your 2 DIMM board really limits you to 32GB unless you can find a 2X32GB kit if you ever wanted to try it.

It's best to install 16GB now and get it over with since it’s going to be more expensive then a 4 DIMM board due to the need for high density RAM.