Look at the writing on the side of the tire. It should tell you the maximum tire pressure right along with information as to the tire size. Sometimes it will have a range.
Here is an example for the Kenda 700C X23 tire I use on the rear of my recumbent trike.
I never bother to actually measure the pressure, just pump them up hard so I can't depress the tire much with my thumb. If I let it get soft I will get the type of pinch flat your picture shows,