I have several ideas.
First, do a search on this site. Traffic light problems abound, as they appear to be the most common application for PLCs, far exceeding slicing pickles, for example.
Second, you need to make a list of all of the inputs and outputs for the system - that is, a detailed list of everything that the PLC is turning on (outputs like Green North, Amber South, etc.) and signals it is receiving (penguin at south east crosswalk, for example.)
Then, you need to go to your text, and find out what makes a timer time, and an output turn on, and a contact close.
Then you need to write a detailed description of each step in the cycle.
Then you need to read the tutorial on this site.
Then you need to replace each event in your description with the corresponding ladder logic command (on = contact closed, for example).