How Would You Solve PV=4000(1-(1+.06)^-9)/.06?

Perhaps the easiest way is to type the expression into a Google search box. The result is
(4 000 * (1 - ((1 + .06)^(-9)))) / .06 = 27 206.7691

If you're going to evaluate it with your own calculator, you start with the inner parentheses.
  1+.06 = 1.06
Then, you perform the exponentiation (use the y^x key)
  1.06^-9 ≈ 0.59189846353
You need to keep as many digits of precision for this as you can, preferably 8 or more, so the answer can be properly rounded to 7 significant figures.
After the exponentiation, you finish the calculation in the outer parentheses by subtracting this value from 1.
  1 - 0.59189846353 = 0.40810153647
In the normal scheme of things, you would then perform the multiplication by 4000 and the division by .06, as these are the order of the operations from left to right. Of course, the commutative and associative properties tell us that we can do these in any order. It might be enlightening or convenient to divide by .06 first so you get a feel for the multiplier being applied to the 4000 principal.
  0.40810153647/.06 = 6.8016922745 (on my calculator)
That times 4000 gives the above answer
  4000*6.8016922745 = 27,206.769098

Rounded to cents, that is 27,206.77.