To simplify this expression, first expand both the squared terms using the formula (a + b)^2 = a^2 + 2ab + b^2.

(a+3)^2 = a^2 + 2(3)(a) + 3^2
= a^2 + 6a + 9

(3-a)^2 = 3^2 - 2(3)(a) + a^2
= 9 - 6a + a^2

Next, expand the middle term:

2(3-a)(a+3) = 2[3(a) - a(a) + 3(3)]
= 2[3a - a^2 + 9]
= 6a - 2a^2 + 18

Now, substitute the expanded squared terms and the expanded middle term back into the expression:

(a+3)^2 + 2(3-a)(a+3) + (3-a)^2
= a^2 + 6a + 9 + 6a - 2a^2 + 18 + 9 - 6a + a^2
= a^2 + 6a + 9 + 6a - 2a^2 + 18 + 9 - 6a + a^2
= a^2 - 2a^2 + a^2 + 6a + 6a - 6a - 6a + 9 + 18 + 9
= 0 + 0 + 0 + 0 + 0 + 0 + 36
= 36

Therefore, the simplified expression is 36.