3.2 ghz quad core, 2.3 ghz eight core, which is more powerful for gaming?

Look up the benchmarks at the passmark web site. 
https://www.cpubenchmark.net/

There is a great deal more to CPU performance than clock rate and number of cores.
In any case Gaming is mostly about your video card. Again, Passmark is the best source for guidance.

Depends on the game and specific make/model of CPU, but as a general rule, the GPU does most of the work when gaming.

However, since you have access to the interweb....figure out the specific CPU's you are trying to compare and google the Bench Marks for them.

depends on what type of games you play, but possibly the quad core

The answer hinges on which processors you're talking about to begin with. Older games and a few newer games don't use a lot of cores, but newer games will use a lot of cores. However with these newer games, having a higher number of cores with lower clock speeds will still hinder performance. 

Also, with gaming the Graphics card does most of the work. Your question about the CPU is mostly irrelevant because a PC with a great CPU and a crappy GPU will still play games like junk.  

Most games prefer higher clock speeds to a large number of cores. That said, simply stating the number of cores and the clock speed isn't sufficient for an accurate rating of a processor's performance. The age / architecture of the processor is also important. 

Answer depends a bit on what games. While some higher end games are now using multiple cores, a lot of games still use only one CPU core to run. Thus a single core would run better at higher speeds. But, Windows uses some of that as well, uses a core or two.

There is a big difference between 3.2Ghz and 2.3Ghz. You would also have to look at things like "turbo" speeds and how many cores run as the CPU heats up. Many multi-core processors either drop speed as they heat up, or run less cores to get higher speeds. That is, very few multi-core CPUs run all cores at the full rated speed, they get too warm.

Bottom line, I suspect these are different processors, different family of CPUs. One cannot compare apples to oranges. The 3.2Ghz sounds more like a gaming processor (without details). But, without specific CPU model numbers, one is guessing. A quad core with Hyperthreading looks like 8 cores to Windows.

You've probably already moved on with this, but GHz isn't a measure of speed for processors. Computer manufacturers love to use it because consumers like numbers, but they aren't very meaningful unless you're comparing two CPUs of the same brand and generation.

You can often find benchmark tests where someone has run more common games on the CPUs you are looking at.

depends on what type of games you play.

Depends on the game, if its a recent game that takes advantage of multiple core then the latter,. if its an older game that uses a single core the former.

What games do you play? older games I would say the former, newer games the later.

depends on what processors you are comparing.
an 8-core Atom will always be slower than a 2-core Core i5, regardless of clock speed.
clock speed only matters in apples-to-apples comparison, and then, other factors affect it, too...
cpubenchmark.net

My gaming rig has a quad-core 3.8 GHz i7 and paired with 32 GB of RAM and a GTX 1660Ti it runs every game that I have bought.

A single core 3 GHZ CPU can run Crisis well with a good GPU.

2.3 is slow regardless of the number of cores , it also depends on the motherboard many cannot handle 8 lanes of data 

Depends on what type of games you play,

choose which on they have a plus or a minus on diferent apps .depends on what the game demands , it could run on iether 4 or 8 core , depend on what type of proccesor , 8 core atom , or 4 core u7 or it could be a ryden 7 processor , best would be the ryden 7 as its designed for games , intel runs business programs better .careful which you choose , either for business or a games machine .