Ошибка ValueError: invalid literal for int() with base 10

Попробуйте так:

from tkinter import *
import time
import random as r


root = Tk()
root.title('Tkinter')
root.geometry('200x200')

num1 = str(r.randint(1, 24))
num2 = str(r.randint(0, 24))

a = str(num1) + ' * ' + str(num2)
b = 'Награда ' + str(r.randint(1,100)) + ' кредита(-ов)!'
c = int(num1) * int(num2)


def question():
    global answer
    global answer_string
    global answer_int
    label = Label(root, text='Решите пример:').grid(row=0, column=0)
    math = Label(root, text=a).grid(row=0, column=1)
    gift = Label(root, text=b).grid(row=1)
    btn = Button(root, text='Проверить')
    btn.bind('<Button-1>', answer_check)
    btn.grid(row=3)
    
    answer = Entry(root)
    answer.grid(row=2)
#    answer_string = answer.get()                              # ---
#    answer_int = int(answer_string)                           # ---

def answer_check(event):

    answer_string = answer.get()                               # +++                   
    answer_int = int(answer_string) if answer_string else -1   # +++
    
    if answer_int == c:
        Label(root, text='True').grid(row=4)
    else:
        Label(root, text='False').grid(row=4)


question()

root.resizable(False, False)
root.mainloop()