The label you cite does not show wire gauge, but it does show amperage rating - in this case, 10 amps. In fact, the amperage rating is really what you want to know, anyway, because that is what you compare to the load you plan to use - in your case, a projector. You need to read the projector label to see what its amperage consumption is. If it does not quote amps but tells you watts, just calculate: Watts = Volts x Amps, and volts is 115 (but use 120 - it's easier to calculate). If mathematical gymnastics is your bag, I usually do something like take watts, divide by 100 (real easy!) to get an overestimate of amps, and any cord able to do that is surely OK. To get closer, reduce the amps overestimate by about 1/7 or 1/8. So if it's a big electric heater rated at 1250 Watts, my overestimate is 12½ amps, and a better estimate is about 11. (The true answer is 1250/115 = 10.90.)
When extension cords are sold the cord is supposed to have its info printed or molded into the outer cover. Sometimes you have to look hard because words just molded into the plastic are not easy to read. But it should say something like "16/3" or "18/2" or "14/3". The teen first number is the gauge, also known as AWG for American Wire Gauge. The single number after the slash is how many wires are inside - 2 for hot plus neutral, or 3 for those two plus a ground wire. Of course, you coulda figured out that last part from how many prongs are on the plug on the end. Some actually specify an amperage rating.
The maximum amperage a cord can handle depends on how heavy the wires inside are (heavier wires carry more current and have a LOWER AWG size number) and on the type of insulating material used. But as a general rule, the ratings are about:
18 AWG = 10 amps
16 AWG = 13 amps
14 AWG = 15 amps
12 AWG = 20 amps
However, if you plan to use a long extension (say, 100 feet or over), use the next-heavier wire gauge if you are close to a load limit. Heavy motors also need a heavier cord because they pull an extra-heavy current for a short time as the first start up, especially if they are already under load (like starting up your lawnmower while it is sitting in long grass). And don't forget, it's the cord length, not the distance between you and the outlet. If you are mowing your lawn (electric mower) using a 100 foot cord, the electricity does no know you are standing right next to the outlet on the side of the house. By the way, most electric lawnmowers pull less than 10 amps under normal running conditions (more when going through heavy grass), so a 14 gauge 100 foot cord is suitable, but a 16 gauge is marginal and 18 gauge is not enough.