In Star Wars movies, it is said that Anakin Skywalker is way older than the age he is supposed to start training, however strangely enough Luke gets his training in his adulthood?
Anakin Skywalker was taken to the Jedi Order for training. At that time, it was unusual for them to train anyone as old as Anakin, for various reasons. The fact that Anakin is so powerful in the Force that they ended up training him anyway. (In hindsight, all the people who said he was too old were probably right.)
Luke was not trained by the Jedi Order; there was no Jedi Order. As far as Yoda knew, Luke was literally the only person left in the galaxy that could be trained as a Jedi. Even then, note that Yoda runs down a laundry list of things wrong with Luke, and his age is on that list:
BEN'S VOICE: So was I, if you'll remember.
YODA: He is too old. Yes, too old to begin the training.
But ultimately, Yoda has to train Luke because there isn't anyone else.