Hi Amy,
to solve this type of question, you will need to find a common base for both sides of the equation
as one of the number is 27 and the other is 9, the common base will be 3
27^(4x) = (3^3)^(4x) = 3^(12x)
9^(x+1) = (3^2)^(x+1) = 3^(2(x+1))
now you will have 12x = 2(x+1), and you can solve for x
Please let me know if you have any questions