A.
Milk 本是不可数名词,按理来讲应该用 how much.但题中有 carrots,在中文里我们叫“量词”,它是可数的,所以这种情况下应该用 how many 来直接修饰 carrots 而不是 milk.
又如：
a.How much meat do you want?
b.How many kilogrammes of meat do you want?