This problem can be solved by addition and subtraction in the first grade of primary school. We can use the concept of "difference" to solve it.

Suppose the price of watermelon is X yuan.

According to the topic, the price of watermelon bought by Xiaoming is cheaper than that bought by Xiaohong in 8 yuan, that is, the price of watermelon bought by Xiaoming is x-8 yuan, and that of watermelon bought by Xiaohong is x-6 yuan. The price of watermelons bought by two people together is cheaper than that bought by one of them, that is, the price of watermelons bought together is 2x-3 yuan.

Therefore, we can list the following formulas:

(x-8)+(x-6)=(2x-3)

Simplify the formula and get:

2x- 14=2x-3

By addition and subtraction, we can get:

- 14=-3

This is wrong, because the left and right sides are not equal. Therefore, this problem cannot be solved by addition and subtraction in the first grade of primary school. Need to use a higher level of mathematical knowledge, such as algebraic equations to solve.