PLT OF PA28 WITH INSTRUCTOR ABOARD WAS INSTRUCTED TO WAIT FOR AN INCOMING TWIN TO THE FBO; THEN TAXI TO THE ACTIVE RWY. THE TWIN TURNED AWAY FROM THE ACFT AND PLT BEGAN TAXI. THE TWIN THEN TURNED BACK AND APCHED HEAD ON. RPTR THEN TURNED AND TAXIED IN WRONG DIRECTION TO AVOID THE TWIN. IN PROCESS OF TURNING WHEN SIGHTING CONSTRUCTION CONES ON TXWY THE WING HIT THE WING OF A PARKED ACFT.

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ON A TRAINING FLT WITH AN INSTRUCTOR AND AFTER START UP; I RECEIVED MY GND CLRNC WHICH INCLUDED WAITING FOR AN INCOMING TWIN TO THE FBO. I WAS THEN TO TAXI TO THE REMAINING ACTIVE RWY SINCE THE MAIN RWY WAS BEING REPAVED. UPON SEEING THE APCHING TWIN MAKE A TURN ONTO A NON CONFLICTING TXWY I BEGAN TO TAXI. THE TWIN SUDDENLY CHANGED DIRECTION AND BEGAN TO APCH ME ON THE SAME TXWY. HAVING ONLY PULLED OUT SLIGHTLY; I WAS ABLE TO CHANGE MY DIRECTION AS WELL AND CONTINUE AHEAD OF THE TWIN ALTHOUGH FORCING ME TO TAXI IN THE WRONG DIRECTION. AS I APCHED THE OTHER EXITING TXWY BOTH ME AND THE INSTRUCTOR NOTICED IT WAS NOT PASSABLE DUE TO THE PAVING CONSTRUCTION CREW'S ORANGE CONES PLACED ACROSS THE RAMP'S TXWY. THE TWIN HAD SEEN THIS AS WELL AND THIS WAS THE CAUSE FOR THE TWIN'S ORIGINAL CHANGE IN TAXI DIRECTION. A POSITIVE EXCHANGE OF THE AIRPLANE CTLS WAS MADE FROM ME TO THE INSTRUCTOR SINCE I FELT UNCOMFORTABLE IN CONTINUING TAXIING IN THE SMALL AREA WITH THE APCHING TWIN. THE INSTRUCTOR TAXIED TO ANOTHER AREA AND IN THE PROCESS OF TURNING AROUND THE R WING OF OUR ACFT CAME IN CONTACT WITH ANOTHER ACFT WING PARKED ON THE RAMP. I BELIEVE THAT THERE ARE SEVERAL FACTORS HERE THAT NEED ATTN. FIRST; WHEN GND OPS ARE NOT NORMAL AS WAS THE CASE WITH THE EXTENSIVE CONSTRUCTION AT THE ARPT; EXTRA VIGILANCE NEEDS TO BE EXERCISED. IN ADDITION; SMALL 18 INCH CONES ARE NOT EASILY SEEN ON A CROWDED RAMP AREA AS BOTH WE AND THE TWIN EXPERIENCED. WHEN PROBS BEGIN TO COMPOUND; THE LIKELIHOOD OF MISTAKES INCREASES. THE TXWY CLOSURE; REROUTING OF NORMAL GND OPS; TWIN'S APCHING AND INDECISIVE ACTIONS AND OUR DESIRE TO CLR THE WAY ALL BEGAN TO ADD UP. INSTEAD OF TRYING TO MOVE AHEAD OF THE TWIN; PROBABLY JUST STOPPING AND RECONSIDERING THE OPTIONS MORE CAREFULLY WOULD HAVE LED TO A MORE POSITIVE OUTCOME.