This is the main issue. Your print statement only executes once. However you want the print statement to run for each line in the file, so a loop is a good choice.
At the start of your program "a = file.read()" reads the entire file into the variable "a". One option is to use a for loop over the lines in the file:
txt = "Prob06.in.txt"
file = open(txt,"r")
for line in file:
state = line.split()
pos = "W"
neg = "B"
...
LED1= int((n - LED2)/4)
print(LED[LED1], LED[LED2])
Notice that from the line "state = line.split()" to print are all indented, putting them inside that for loop.
Here is my complete rewrite of your program for your perusal (and because I want to look/feel clever). It is obviously different from your program, so don't turn it in as your own homework:
STATES = {"BADGER": 0, "MUSHROOM": 1}
LED = ("off", "red", "green", "blue")
with open("in") as f:
for ln, line in enumerate(f):
try:
bits = [STATES[i] for i in line.split()]
led1, led2 = 2*bits[0] + bits[1], 2*bits[2] + bits[3]
print(LED[led1], LED[led2])
except:
print(f"Bad line: {ln}")