A discount is part of the price
A shop sells a game at 20% off. The full price is the whole, 100%. Cut it into 10 equal parts, and each part is 10% of the price, so 20% is 2 of the parts. Those 2 parts are the discount: the amount the shop takes off.
The full price is cut into 10 parts of 10% each, and the 2 colored parts are the 20% taken off.
What is left is what you pay
Take the 2 parts away and 8 parts are left: 100% − 20% = 80%. You pay 80% of the full price. The discount and the part you pay always make the whole price together: 20% + 80% = 100%.
After the 20% comes off, 8 of the 10 parts are left: 80% of the price.
On a real price
The game costs $50. First find the discount. 10% of 50 is 50 ÷ 10 = 5, so 20% is 2 × 5 = 10. The discount is $10. Then take it off the price: 50 − 10 = 40. You pay $40.
Check it with the part you pay. 80% is 8 parts of $5 each, and 8 × 5 = 40, so the price after the discount is $40 either way.
Each part is $5. The full price is 10 parts, $50; after the discount 8 parts are left, $40.
Any percent off
A jacket costs $80 and is sold at 15% off. Build 15% from 10% and 5%. 10% of 80 is 8, and 5% is half of that, 4. So 15% of 80 is 8 + 4 = 12. The discount is $12, and you pay 80 − 12 = $68.
The bar is the $80 price, with the percent scale under it. The discount, $12, reaches 15% on the scale.
Three mistakes
The discount is not the price you pay. At 20% off $50, the $10 is what comes off, and the shop still asks for $40.
A discount never goes on top. 50 + 10 = 60 would make the game cost more than its full price.
And 20% off is not $20 off. 20% is a share of the price: 20% of $50 is $10, while 20% of $80 is $16.