On April 25, 2014, about 1825 central daylight time, a Piper PA-34-200 multi-engine airplane, N56755, was substantially damaged during landing at David Wayne Hooks Airport (DWH), Spring, Texas. The three occupants were not injured. The airplane was registered to BAT Aviation, Inc.; Spring, Texas, and was being operated by United Flight Systems, Inc.; Spring, Texas. Day visual meteorological conditions (VMC) prevailed at the time of the accident and a flight plan had not been filed for the 14 Code of Federal Regulations Part 91 instructional flight.The flight instructor was manipulating the flight controls and demonstrating a short-field landing. After the airplane touched down at about 90 mph, the flight instructor retracted the flaps and then discovered the right brake pedal went full forward and was not slowing the airplane. He proceeded to pump the brake several times to try and build pressure in the lines, but was not successful. The pilot receiving instruction checked his brake pedals and confirmed the right brake failure. The flight instructor reported that he then shut down both engines when the airplane's speed was about 60 mph. Directional control was lost and the airplane drifted off the left side of the runway and impacted a ditch at an estimated impact speed of about 20 mph resulting in substantial damage to the lower aft fuselage and lower forward empennage. A photograph of skid marks of the main gear tires over the asphalt pavement showed that the skid marks for the left main gear tire seemed to be darker than the skid marks for the right main gear tire which were lighter in intensity. An examination of the brakes on the following day by a Federal Aviation Administration Inspector did not disclose a problem with the right brake, however it was unclear whether the brake system had been serviced or repaired following the accident. At 1753, the official surface weather observation site at DWH, reported wind from 120 degrees at 5 knots, visibility of 10 miles, and few clouds at 6,500 feet. Data from the National Oceanic and Atmospheric Administration showed that, at the accident location, at 1825, the altitude of the sun was about 18 degrees above the horizon and the azimuth of the sun was about 275 degrees. Apparent sunset occurred at 1956.