The good is not a giffen good. These goods have a positive elasticity of demand. Yours has a negative one, by assumption. It cannot yield a giffen good at all.
The error is in the negative sign that you (and also Thomas's answer) assumed.
The formula for the elasticity is:
$$ e_d = \frac{\Delta Q}{\Delta P}\frac{P}{Q}$$
The negativeness of the elasticity is given by the sign of the derivative (a price increase leads to a fall in quantity demanded; the contrary in a Giffen good).
In your example, assuming as starting point $Q_1$ and $P_1$ (you could alternative use the end point, or the arc elasticity; see here), you get:
$$ -8 = \frac{Q_2 - 800,000}{12}\frac{24}{800,000}$$
Which yields
$$Q_2 = -2,400,000$$
This is, in effect, a negative quantity. To see why this is the case, rewrite the elasticity function as follows:
$$ e_d \frac{\Delta P}{P_1} = \frac{\Delta Q}{Q_1}$$
This is, the percentage change in the quantity is equivalent to the percentage change in prices times the elasticity.
Replacing the numbers, you get:
$$ -4 = \frac{\Delta Q}{Q_1}$$
This is, the quantity falls by 400% percent!. That is why it becomes negative (from 800,000 to -2,400,000).
The origin of the problem is the massive change in price (50%) together with the massive elasticity of demand (-8), which gives the total change in quantity ($50\% \times -8 = -400\%$). A less dramatic combination would yield a positive $Q_2$.