We can solve this problem using similar triangles. The height of the man can be determined by setting up a proportion between the lengths of the pole and the length of its shadow, and the height of the man and the length of his shadow.

Let`s denote the height of the man as h. According to the given information:

Length of the pole = 6 m

Length of the pole`s shadow = 8 m

Length of the man`s shadow = 2.4 m

We can set up the following proportion:

(height of the man) / (length of the man`s shadow) = (length of the pole) / (length of the pole`s shadow)

h / 2.4 = 6 / 8

Cross-multiplying, we get:

h * 8 = 2.4 * 6

Simplifying, we find:

8h = 14.4

Dividing both sides by 8, we get:

h = 14.4 / 8

Calculating, we find:

h ? 1.8

Therefore, the height of the man is approximately 1.8 meters. Thus, the correct option is 1.8m.