Both AMD Ryzen processors and Intel Core processors are available in either 6 or 8 cores, depending on what price level and generation you are looking at. Another thing to consider is whether the processor has SMT/Hyperthreading, which can allow it to better handle an additional thread per core for heavily multithreaded tasks.
The Ryzen 3600 offers 6-cores and 12-threads with performance that tends to be quite close to an i7-8700 with a similar 6-core/12-thread core configuration, only with a price that's over $100 less, which is a good part of why it is often recommended. Intel's i5s offer 6-cores for a similar price, though they lack SMT, being only 6-core, 6-thread processors.
8-core processors are available from both AMD and Intel as well, though they are priced in the $330+ range for current-generation models. Again, AMD's 3700X offers SMT for 8-cores with 16-threads, while Intel's 9000-series i7s do not, offering 8-cores, but with only 8-threads. Those i7s are slightly faster per core though, and have enough cores where the lack of SMT isn't currently a significant issue for gaming. So, both the i7-9700K or the Ryzen 3700X could be considered reasonable options, though the i7 is less efficient and will require better cooling, again making it cost a fair amount more. And to get 8-cores with 16-threads on an Intel processor right now, you would need to move up to an even more expensive and power-hungry i9, which are not attractively priced in my opinion.
So, the reason you see Ryzen processors getting recommended a lot is that they currently tend to offer better value, and their inclusion of SMT may make them the better performers down the line as games become more heavily multithreaded. As far as performance in current games goes, they should all perform fairly similar in most recent games when paired with a card like a 2060.