Question 847510
Notice that we are given two sides with its included angle.

Thus the area =  1/2 *a*b * sin(C)

12 = 1/2 * a*b*sin(30 degrees)

b = a -2

12 = 1/2 * a*(a-2)*sin(30 degrees)

12 = 1/2 * a*(a-2) * 1/2

48 = a*(a-2)

48 = a^2 - 2a

a^2 -2a - 48 = 0

(a+8)(a-6)= 0

a = 6

b = 4

So we have that a =6, b=4, we need to find c.

Law of cosines to finish this off:

c^2 = a^2 + b^2 - 2ab*cos(C)

c^2 = 6^2 + 4^2 - 2*6*4*cos(30 degrees)

c^2 = 36 + 16 - 48*(sqrt(3)/2)

c^2 = 10.43

c = 3.23

a = 6, b =4 , c = 3.23