Recall that r^2 = x^2 + u^2 and theta = arctan(y/x).
With the limits you need to basically look at lower and upper limits of x and y and substitute the values of theta and r given those limits.
When y = 0 what does r equal? What about when y = SQRT(36 - x^2)?
It might help you to first draw your original region of integration on some paper and then use this to derive your region in terms of polar co-ordinates.
If you have a circular region, then r is constant. If it changes, then see how it changes with regards to the angle theta.
Also remember that in multivariable substitutions, you need to calculate the Jacobian.