That is a hard one, to draw the state diagram of a Car Park Elevator control system, and then make a ladder diagram for an unknown brand and model of Programmable Logic Controller.
I have not seen anyone here successfuly do this one yet, or at least they didn't say if they got it done. Maybe you will be the first to post your solution?
A guess from reading between the lines is that it is for some model of Siemens PLC, and you should then use some version of Siemens programing software to write the ladder logic.
A place to start is with the given 6 States in the problem:
1st: Waiting State, the most important and the FIRST ONE, not the 6th one as listed. The Elevator PLC will spend most of its time doing this, until someone somewhere (on floor or in car) presses a button.
2nd: Moving UP or Moving Down?
_ 2a: Moving UP
_ 2b: Moving DOWN
3rd: Car Gate Closing
4th: Car Stop
5th: Car Gate Opening
Repeat: Car Gate Closing
Repeat: Moving UP or DOWN
Repeat: Car Gate Opening