Q: Intestinal bacteria synthesize a large amount of Vitamin K. Taking broad spectrum antibiotics can destroy how much of that capacity?

Answer: 2/3rd

Taking broad-spectrum antibiotics can reduce vitamin K production in the gut by nearly 75% in people compared with those not taking these antibiotics.

Reference

Conly, J; Stein K (1994). "Reduction of vitamin K2 concentrations in human liver associated with the use of broad spectrum antimicrobials". Clinical and investigative medicine. Médecine clinique et experimentale 17 (6): 531–539.