Let's assume that the number of goats in the paddock is G and the number of chickens is C. Then, we can create a system of two equations based on the information given:
G + C = 67 (equation 1: the total number of goats and chickens is 67)
4G + 2C = 166 (equation 2: the total number of legs is 166)
We can solve this system of equations for G, which represents the number of goats in the paddock. To do this, we can use the substitution method.
From equation 1, we can solve for C:
C = 67 - G
Then, we can substitute this expression for C into equation 2 and solve for G:
4G + 2(67 - G) = 166
4G + 134 - 2G = 166
2G = 32
G = 16
Therefore, there are 16 goats in the paddock.