To simplify the expression (x+3)^2 / (2x-4) : (3x+9) / (x^2 - 4), we can follow these steps:

First, simplify the numerator of the first fraction:
(x+3)^2 = (x+3)(x+3) = x^2 + 6x + 9

Simplify the denominator of the first fraction:
2x - 4 = 2(x - 2)

Simplify the numerator of the second fraction:
3x + 9 = 3(x + 3)

Simplify the denominator of the second fraction using the difference of squares formula:
x^2 - 4 = (x + 2)(x - 2)

Now, we can rewrite the expression as:
(x^2 + 6x + 9) / 2(x - 2) : 3(x + 3) / (x + 2)(x - 2)

Next, we can simplify further by multiplying by the reciprocal of the second fraction:
(x^2 + 6x + 9) / 2(x - 2) * (x + 2)(x - 2) / 3(x + 3)

This simplifies to:
(x^2 + 6x + 9)(x + 2) / 2 * 3(x + 3)

Further simplifying:
(x + 3)(x + 3)/ 6 = (x + 3)^2 / 6

Therefore, the simplified expression is: (x + 3)^2 / 6.