Adding memory is cheap and effective on a machine that is short of it. There are two ways it goes wrong, and both are avoidable.
Check what you have first
Open Task Manager on Windows, go to Performance, then Memory. It shows total capacity, how many slots are in use, the generation, and the speed it is running at.
That last figure is worth noting. If it is well below what your modules are rated for, you may not need to buy anything at all; enabling the EXPO or XMP profile in firmware may give you what you were missing.
Mixing modules is unpredictable
Adding modules to existing ones frequently works and sometimes does not, even when the specifications appear to match. Memory modules vary in the specific chips they use, and a memory controller has to find timings that suit all of them at once.
When it fails, it usually fails by running everything at a lower speed, and occasionally by not starting at all.
The reliable approach is to replace rather than add: buy a kit of the total capacity you want, sold and tested together. Kits are tested as a set, which is what you are paying for.
Why filling all four slots can be a step backwards
On most consumer platforms, populating all four slots makes signal integrity harder and the system compensates by lowering the memory speed.
So going from 2 × 16 GB to 4 × 16 GB can leave you with double the capacity running below the rated speed. If you were not short of capacity, that is a net loss.
Check the board limits before ordering
Two limits catch people. The maximum capacity the board supports, which is on the manufacturer specification page, and the maximum capacity per module, which is sometimes lower than you would expect on older boards.
A board rated for 64 GB across four slots may not accept two 32 GB modules, because it is specified for 16 GB per module. The total is right and the configuration is not.
Also check the generation. This sounds obvious and is a genuinely common mistake, because DDR4 and DDR5 modules look similar in a photograph and board models frequently exist in both variants under nearly identical names.
Fitting it
Power off and switch off at the wall. Open the clips at each end of the slot, line up the notch, and press down firmly at both ends until the clips close by themselves. It takes more force than feels comfortable.
Check the manual for which slots to use with two modules. It is usually the second and fourth from the processor, not the two nearest.
If you have a large air cooler, check module height clears it. Low profile modules exist for this reason, and a tall heat spreader can mean raising the cooler fan or not fitting it at all.
After starting, enable the memory profile in firmware, then confirm the reported speed matches what you bought.
If it will not start afterwards
A machine that was working and now does nothing after a memory change is almost always a seating problem. Memory needs more force than people expect, and a module that looks level can have one end not fully home.
Remove everything and fit one module in the slot the manual specifies for single-module operation. If it starts, add the rest one at a time.
If one particular module prevents startup in any slot, that module is faulty. If a slot fails to work with any module, the slot or a bent socket pin is the problem.
Clearing CMOS also helps where a previous memory profile no longer suits the new modules. The board then starts at conservative defaults, and you re-enable the profile afterwards.