Jill asks each of her classmates to choose a number, then multiply the number by , add 2...

Jill asks each of her classmates to choose a number, then multiply the number by , add 2 to the product, multiply the result by , and then subtract 14. Finally, each student is asked to divide the result by 6 and record the answer. When Jill gets an answer from a classmate, she just adds 3 to it in her head and announces the number that classmate originally chose. How did Jill know to add 3 to each answer?