Step 1: Recall what hypothalamic hypogonadism means.
Hypothalamic hypogonadism (also called hypogonadotropic hypogonadism) happens when the hypothalamus fails to release enough gonadotropin releasing hormone (GnRH). Without GnRH, the pituitary does not make enough LH and FSH, so the gonads never get stimulated.
Step 2: Match each option to its actual defect.
Frohlich syndrome (adiposogenital dystrophy) does cause obesity with hypogonadism, but it comes from a general hypothalamic tumor or lesion, not a specific GnRH neuron defect.
Foster Kennedy syndrome is optic atrophy in one eye with papilledema in the other, caused by a frontal lobe tumor pressing on the olfactory groove. It has nothing to do with the reproductive axis.
Fragile X syndrome is an X linked repeat disorder that causes intellectual disability and large testes in males; it is not a cause of hypogonadism.
Step 3: Focus on Kallmann syndrome.
Kallmann syndrome happens when the neurons that should make GnRH fail to migrate from the olfactory placode into the hypothalamus during fetal development. This gives isolated hypogonadotropic hypogonadism, classically together with anosmia or a poor sense of smell, since the olfactory bulbs also fail to form properly.
This is a true hypothalamic cause of hypogonadism, unlike the other three options.
Final Answer:
Kallmann syndrome is the condition that causes hypothalamic hypogonadism.
\[ \boxed{\text{Kallmann syndrome}} \]