I have a little problem that i can not solve with simple relays and have never messed with arduino before so I am not sure if it is feasible or not with it and am looking for some advice, and if it would be an expert type project or feasible for a beginner.
I have two automatic swing doors and four momentary pushbuttons, one button for each state the combined doors can be in. So i would need 4 inputs and 2 outputs. The inputs would be a N/O momentary signal from the pushbuttons and the outputs would need to be able to latch closed to send the signal to keep the door open until another button is pressed for a different operating state. Open output equals closed door, closed output equals open door.
State 1/Button 1- Both doors open
State 2/Button 2- Both doors closed
State 3/Button 3- Door 1 open, Door 2 closed
State 4/Button 4- Door 1 closed, Door 2 open
If this is possible, what would i need.?.?.?
Thanks!!! 
If this is possible
Yes, almost trivial.
The inputs would be a N/O momentary signal from the pushbuttons
Wire these between input and ground, and enable the internal pullup resistors when using the pinMode call in the setup function.
the outputs would need to be able to latch closed to send the signal to keep the door open until another button is pressed for a different operating state.
That happens automatically. An output only changes when you code tells it to.
However the output while being 5V should be limited in the current you draw from it to about 20mA. This is just a signal. You will need some sort of driver to take that 5V signal and convert it into the signal that you need to drive your door mechanism.
How many door actuators and how do you intend they operate?
2 buttons can give 4 states.
I'd use a 3 position switch set sideways to select left door, both doors, right door and a 2 position switch set vertical to select open or closed.
The Arduino would read the switch positions and knowing the state of each door from sensors and variables tracking what is being done at the moment chooses what to do "now". Yes, Arduino clock functions let us use time in code -- one place is to not obey switch-flicking while still being able to stop either door ASAP.
The code to do all that requires some form of non-blocking, the do-many-things-at-once lesson and the state machine lesson shown here on the forum and around on the web are the keys to coding this. It may seem easy to me but for you there are projects you need to do before you can do this one. Watching more than one pin (button, sensor) at a time is the do-many.