How can we find the height without involving trig?
It’s not that straightforward and the real question is do you really want to do it? The height is just 6 \sin(55^{\circ}).
For this problem, we don’t really need the height. We just need to estimate / understand what’s going on:
Imagine dropping a perpendicular from C down to say point P. So a triangle DCP is formed with hypotenuse (DC) as 6 units. Since Its a right angle triangle the height of this triangle (CP, which is also the height of the parallelogram) has to be less than 6 units. So in any case the area of the parallelogram is always less than 24 (since for it to be 24, the height must be 6 and as understood above it always will be less than 6 units.)