Greetings Shapcrook.
This appears to be a homework problem. While we don't provide the final solutions for homework problems, we do provide help in solving them. If its not a homework problem then this will hopefully still be helpful.
You have two states.
In state 0 the outlet valve is open, the inlet valve is closed.
In state 1 the outlet valve is closed, the inlet valve is open.
Pressing the start button transitions you from state 0 to state 1. Pressing the stop button or having the tank full transitions your from state 1 back to state 0.
Since its a tank filling, lets call the state Filling. When Filling = 0 we are not filling the tank, and when it is 1 we are filling the tank.
If we create a truth table for this we get
Filling | Inlet_Valve | Outlet_Valve
--------+-------------+--------------
0 | 0 | 1
--------+-------------+--------------
1 | 1 | 0
Looking at the table we see that
Outlet_valve = NOT Filling
and
Inlet_Valve = Filling.
Now all we need to define now is the logic for the state, or Filling, which can be 0 or 1. In plain language, when we push the start button we want FILLING to change to a 1 and we want it to remain a 1 until the stop button is pushed or the tank is full. If we write that statement as a boolean equation we get
FILLING = (Start_Button OR FILLING) AND NOT Stop_button and not Tank_Full.
From here you should be able to construct three rungs of ladder logic that implement the flow chart.
Extra Credit: Reduce this to two rungs and eliminate the need for a bit to define the state (Hint: Outlet_Valve = Not Inlet_Valve and Inlet_Valve = Filling)