Welcome to the Forum!
Do be aware that you should not be "looking for" solutions but "creating" solutions to this homework problem. If you happen to "find" something, you will learn nothing but how to cheat by copying other people's effort. This may be enough to get you through a lesson or a class, but not a life.
And remember, your teacher's Googling skills are probably equal to your own.
You did ask a legitimate question, which deserves a legitimate answer, however.
First off, the PLC never does anything randomly. It always does what it's told, which may or may not be what you intend.
If you look at rung 8, you'll see reference to "T4:2.ACC.1". This is a bit in the accumulated time of the timer. Remember your binary:
Value | Binary
0 = 0 0 0 0
1 = 0 0 0 1
2 = 0 0 1 0
3 = 0 0 1 1
4 = 0 1 0 0
The /1 bit is the second from the end, thus is true (making -| |- true) when the value is 2 or 3 (or 6 or 7 ....), and false (making -|/|- true) when the value is 0, 1, 4, 5, etc.
The TON instruction is driven by the -|/|- of the timer's own DN bit. Thus, because of the way the TON "thinks", when the time is up, the DN bit gets set, making DN true and thus the -|/|- NOT true, which resets the timer, including the DN bit, which then makes -|/|- true, and the timer starts from scratch. This is a very common technique.
Thus the timer counts 0-1-2-3-(4 back to 0), changing every 0.1 sec.
Thus for the first 0.2 sec, -|/|- T4:2.ACC.1 will be true, making the Up Flag true and the Down Flag false. Then during the next 0.2 sec, it will be the other way around.
In other words, the Up and Down flags blink alternatively and mutually exclusively.
You may already understand this; if so, pardon my assumption that you did not. You're question was: "It's kinda weird but is it safe to use in the real world?"
It's not all that weird; variants on this technique are quite common in making lights blink.
The use of latches allow the left-hand side of the rung to go false, and the PLC "remember" what it's supposed to do -- probably drive the elevator up or down once a button has been pressed. It would certainly be strange for the elevator to start going up, then if someone happened to call from a lower floor while it was travelling, for it to stop going up and head down.
As for "is it safe"? That's going to depend on the rest of the program. Without that, there's no way to tell. There's nothing inherently UNsafe about the code snippet, but without the rest of the code, it's impossible to judge.
If you post YOUR code and have questions as to why it isn't doing what you expect, we're usually only too happy to help. But please don't ask us to do anything for you. We're here to teach, but that usually means sitting on one's hands after pointing the student in the general direction of the answer.
Good luck!