Hey guys can u tell me if the top is correct if its not can u show me step by step what to do and what the answer will be and can u guys tell me what explanation i should write in the bottem

You have the right idea and you are close to the correct answer. However that's not what your teacher is looking for in terms of steps.

The starting inequality is 
She starts off selling 8 buckets. Then she sells b more to get a total of b+8
This total must be 20 or larger which is why I set b+8 greater than or equal to 20

Solve for b by subtracting 8 from both sides







So she needs to sell at least 12 more buckets to reach her goal

If you graphed this on a number line, then you would draw a closed circle at 12. Then shade to the right of the close circle.