The HyperX should work but keep in mind that Dell systems are rather picky about RAM and the most compatible are from Crucial as listed below. Do not use the second type listed as that is Kingston Value RAM and is budget RAM. Always look for high quality RAM for any Dell systems.

https://www.crucial.com/usa/en/compatible-upgrade-for/Dell/optiplex-3060-micro

If you look at the link I mentioned, Crucial does sell 2666 RAM for that system. And you did not mention which CPU you have in the 3060. Note the information from the Dell support page.

Speed

•2666 MHz

•2400 MHz on Celeron, Pentium, and i3 processor

@JOcean 

Several posters here say that kingston ram is just no good, especially that marketed as "value ram".

Does anyone actually know what the root cause of the problem is? I would think that either the memory doesn't meet it's specs, or dell's (intel chips) doesn't meet the relevant specs. (This is naturally assuming there are no failed parts in the memory module or the perfidious dell computer). So there should be no reason this must remain forever a mystery.

Does anyone know who makes kingston's Dram chips? I have a kingston module that works fine, but I didn't think to examine it closely for the chip markings. I figure they probably contract-buy their chips from a large asian semiconductor company. If so, there could be lesser known brands that also refuse to function with dells.

@bradthetechnut  has also mentioned having problems with hynix ram modules. I wonder if hynix could be a chip supplier to kingston? I have 4 hynix modules (no longer used) and another 2 hynix modules currently in use. All of these were used modules, and still function fine. But perhaps there is a systematic error in some of their production which has not been discovered yet. Like with the famous Intel SATA time bomb on the early sandy bridge chip sets.

Exactly why I advised against using Value RAM as Dell systems need a top quality proven compatible RAM. Hynix is a more interesting topic. I have an HP laptop with Hynix and it works well. But my favourite is RAM (G. Skill comes to mind) with Samsung chips. Micron also is quality and used in many of the Dell systems (and I believe used in Crucial memory).

@JOcean 

@JOcean

Micron is the same  company as ballistix and crucial. Same company, different marketing names.

They are much better than hynix and kingston, and will actually work in dell computers.

Yes; Dell is the very finest quality, and so it naturally requires the  highest quality proven compatible authorized upgrades. Nothing less will work. You just can't put a farmer's plow mule's shoes on a racehorse and expect to win the kentucky derby.