Answer:
No, it's not correct
Explanation:
Let's suppose the initial price by which she purchases is P. if she marks up the price by 20%, retail price (RP) is 1.2*P
If then, she marks down the price by 20%, it's the same than multiplying it by 0.8. So the promotion price (PP) would be:

0.96*P is less than P, the initial price by which she bought it, not the same price.