This boy has achondroplasia, which is caused by an autosomal dominant mutation in Fibroblast Growth Factor Receptor 3. FGF signaling is needed for proper cartilage function, and without it, the long bones of the body will not grow because the growth plate (made of chondrocytes) does not function. However, bones that undergo membranous ossification, like the bones of the head, will grow normally. This results in the patient having short extremities with a normal size trunk and large head relative to the limbs.

The answer is not osteoclast activity because that would be referring to osteopetrosis in which there is a defect in osteoclast activity and you have thick dense bones that fracture easily. Improper osteoclast activity could also refer to Pagets disease of the bone aka Osteitis deformans but I don't think that would present this young and would be more associated with bone remodeling problems and an increase in hat size, etc.

The head size isn't increased it just looks like a large head in comparison to the dwarfism because achondroplasia doesn't affect membranous bones of the head. Increased growth hormone synthesis would be acromegaly I think but that is seen in adults. Low nasal bridge = saddle nose.

TMI but in FA there's something called Laron syndrome which is AR, and a defective GH receptor so you have increased GH and would also see dwarfism and a saddle nose and prominent forehead but a small head circumference.