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import Tkinter
import random

class colourgame():

 colours=['Red','Blue','Green','Pink','Black', 
 'Yellow','Orange','White','Purple','Brown']
 score=0
 timeleft=30

 def __init__(self):
 root = Tkinter.Tk() 
 root.title("COLORGAME") 
 root.geometry("375x200") 
 instructions = Tkinter.Label(root, text = "Type in the colour of the words, and not the word text!", font = ('Helvetica', 12)) 
 instructions.pack() 
 scoreLabel = Tkinter.Label(root, text = "Press enter to start", font = ('Helvetica', 12)) 
 scoreLabel.pack() 
 timeLabel = Tkinter.Label(root, text = "Time left: " +str(self.timeleft), font = ('Helvetica', 12)) 
 timeLabel.pack() 
 label = Tkinter.Label(root, font = ('Helvetica', 60)) 
 label.pack() 
 e = Tkinter.Entry(root) 
 root.bind('<Return>', self.startGame()) 
 e.pack() 
 e.focus_set() 
 root.mainloop()

 def startgame(self,event):

 if self.timeleft==30:
 self.countdown()
 self.nextcolour() 

 def countdown(self):

 if self.timeleft > 0: 
 self.timeleft -= 1
 timeLabel.config(text = "Time left: "+ str(self.timeleft)) #explain
 timeLabel.after(1000, self.countdown) 

 def nextColour(self): 

 if self.timeleft > 0: 
 e.focus_set() 
 if e.get().lower() == colours[1].lower(): 
 self.score += 1
 e.delete(0, Tkinter.END) 
 random.shuffle(colours) 
 label.config(fg = str(colours[1]), text = str(colours[0])) #explain
 scoreLabel.config(text = "Score: " + str(self.score)) 


obj=colourgame()
obj.startGame()

The error that arises is:

AttributeError: colourgame instance has no attribute 'startGame'

Please someone explain me the reason.

python is case sensitive. your issue is here:

obj=colourgame() 
obj.startGame() #this should be obj.startgame() because you defined it all lower case not CamelCase

you have the same issue in the __init__() definition in this line root.bind('<Return>', self.startGame()) which should be root.bind('<Return>', self.startgame())