Can you use Fritzing to create a 4 layer pcb?
Also, in real life, what is the maximum limit of layers we can use to create pcbs? is it 4 layers?
As has already been said PCBs come in lots of layer counts. The same can be said for soldermask color, material, thickness, copper weight, and finish.
Fritzing only supports two copper layers, you can see an example at the Fritzing's View options tutorial and it only has the copper 0 and copper 1 layers available for display. As for the maximum numbers of layers a PCB can have I'm not sure, but a local company I've used in the past (but not for this many layers) Entech Electronics advertise up to 26 layers.
As others have mentioned Fritzing is not a very serious tool and you would be better to have a look around at other solutions most of which are better and faster to use once you get used to them. Another one worth a look at is Eagle that is free for limited non-commercial use and fairly affordable for commercial use.
I don't know what you can do in Fritzing - no one in their right mind uses it for anything more than creating little doodles for people that don't know how to read a proper schematic (i.e., children).
PCBs can be made in many many layers. 2, 4 and 16 layers are common, though even higher are possible.
Fritzing only supports two layers, which is sufficient for most hobby uses, the target audience for the tool. In fact, I've designed a fair few one-sided boards, back when it was more cost effective to etch my own. Four layers are plenty for hobbyist use and even a lot of professional products.
My company makes products comparable in size and density to a motherboard, and I believe we typically use between 10-14 copper layers. Mostly you need that many layers when working with chips with a lot of I/O, like processors or FPGAs. You just plain need the layers in order to get everything where it needs to go without using tons of space. Also, when you make complex boards with signals at gigabit speeds, there are a lot of layout restrictions that are necessary to avoid crosstalk, meet regulatory emission requirements, dissipate heat properly, etc. It's a difficult enough problem that we employ people who specialize in just layout and routing.
PeterJ pointed out a manufacturer that will go up to 26 layers. You might be able to do 4-5 more than that, but you're starting to hit practical physical limits with warping and such. I don't know any low-cost prototype board houses who will do more than 4 layers, though. If you want more layers, you have to be prepared to spend a lot and/or order in high volumes.