Value is the numerical amount of something, sometimes as a specific amount.
eg This car has a value of $15,000.
eg Determine the value of the car (the value becomes a variable, x = value)
Quantity is the amount of something, usually without expressing it in a specific amount
eg A container holds a small quantity of liquid. (we do not know exactly how much "small" means")
eg Determine the quantity of liquid in the container. (the quantity becomes a variable, x = quantity)