It is probably easiest NOT to re-arrange the expression, but to do the vector addition first:
( -2, 1, 2)T · ( (3, -1, 4)T + ( -2, 1, -2)T ) = ( -2, 1, 2)T · (1, 0, 2)T
= -2*1 + 1*0 + 2*2 = -2 + 4 = 2
Other times it is easiest to re-arrange the expression.