The correct answer is Option B: B and D only. Here's why:

Let's break down each STD and its curability:

A. Genital Warts: Caused by the Human Papillomavirus (HPV), genital warts are not always completely curable. While treatments like topical medications or surgical removal can eliminate visible warts, the virus itself may remain dormant in the body and reactivate later.

B. Genital Herpes: This viral infection caused by the Herpes Simplex Virus (HSV) is not curable. Antiviral medications can suppress outbreaks and reduce transmission, but the virus remains latent in the body, capable of recurring.

C. Syphilis: A bacterial infection, syphilis is completely curable with appropriate antibiotic treatment, especially in its early stages. However, untreated syphilis can cause serious long-term health complications.

D. Hepatitis-B: This viral infection is not curable, although a vaccine can prevent infection. Hepatitis-B can become chronic, potentially leading to liver damage and cirrhosis.

E. Trichomoniasis: A parasitic infection, trichomoniasis is completely curable with antibiotics.

Therefore, the only STDs from the list that are not completely curable are genital herpes (B) and hepatitis-B (D).