valid = False;
While[! valid,
 try = Map[Total[TakeLargest[#, 3]] &,
   RandomInteger[{1, 6}, {6, 4}]];
 If[Total[try] > 75 && Count[try, _?(GreaterEqualThan[15])] >= 2,
  valid = True;
  ]
 ]
{Total[try], try}