split the inequality into two:
(-4x+14)>6 & -(-4x+14)>6
solve:
(-4x+14)>6
-4x>-8
x<2
(symbol changes when ÷/× by negative for inequalities.)
-(-4x+14)>6
-4x+14<-6
-4x<-20
x>5
the answers are x<2 and x>5, so you would write your answer like this: (-∞,2) ∪ (5,∞)