The Horodok synagogue was destroyed during World War II when it was ransacked and burned by the Germans. This was a common fate for many synagogues across Europe at the time, as they were often targeted for desecration and destruction by the Nazi occupiers. The synagogue in Horodok (Davyd-Haradok) did not escape this tragic fate.
For more detailed information, you can refer to Shtetl Routes - NN Theatre, which notes that the synagogue was destroyed during the war.
Here is an image illustrating such destruction:
Which synagogues are still extant and why did most get destroyed?
How were the synagogues in Vishnyeva and Zabłudów destroyed during World War II?
How did the synagogue in Bechhofen get destroyed during the Nazi era?
How did the historical events, such as uprisings and wars, impact these synagogues?