If you know that angles B and C are the same, that means sides AB and AC are the same too, bc if they were different lengths, the angles would be different.
If AB = AC, you can make the equation 4x+4 = 6x-14 and solve for x.
First I would move all the xs and numbers to separate sides, so subtract 4x from both sides and add 14 to both sides (this avoids negative numbers). This would give you 18 = 2x
From here just divide both sides by 2 to get the x by itself, to get 9 = x.
After you have the x value, just plug it into the AC side function (6x-14) to get 6(9)-14 = 54-14 = 40, which is the length of AC