Starting equation: ( ¼ )x - 6 = -( ¾ )x +14

Add 6 to both sides, to get:
( ¼ )x - 6 + 6 = -( ¾ )x + 14 + 6
( ¼ )x = -( ¾ )x + 20

Add ( ¾ )x to both side:
( ¼ )x + ( ¾ )x= 20

x = 20