What is greater (24 - 12√3) or π?

√3 ~= 1.732
24 - 12√3 = 3.215...

π = 3.1415926...

Thus, (24 - 12√3) is greater.

By calculator, (24 - 12√3) = 3.215390309 (approximately)

π = 3.14159 (approximately)

Therefore (24 - 12√3) > π

Do you mean 2π? Unit circle with radius 1 has circumference 2π.

(24 - 12√3) ... is a bit more than π

If π denotes the circumference of the unit circle, then
π > 24 - 12√3.
http://en.wikipedia.org/wiki/Unit_circle

If π denotes half the circumference of the unit circle, then
(24-12√3) = 12(2-√3)*(2+√3)/(2+√3) = 12/(2+√3) >
12/(2+√3.24) = 12/3.8 = 60/19 = 3 3/19 > 3 3/21 =
3 1/7 = 22/7 > π
http://en.wikipedia.org/wiki/Pi

Edit:
tan(x)>x for any real x in the interval (0,π/2] ==> tan(π/12)>π/12
Since tan(π/12)=2-√3 ==> 2-√3>π/12.
Multiply the above inequality by 12 ==> 24-12√3>π.

I hope you don't need a drawing showing tan(x)>x for any real x in the interval (0,π/2]
or the graphs of f(x)=tan(x) and f(x)=x,
because it's well known that
[tan(x)]'=1/cos²x≥1=(x)' for any real x ==>
f(x)=tan(x) increases more rapidly than f(x)=x for any real x except for x=kπ,
where k is a whole number
and since tan(0)=0 ==>
tan(x)>x for any real x in the interval (0,π/2].

24 - 12√3
= 24 - 12(1.732)
= 3.215

π
= 3.142

∵ 3.215 > 3.142
∴ (24 - 12√3) > π

(24 - 12√3) is greater.