**12**

5 consecutive multiples of 3 are: 3x-6, 3x-3, 3x, 3x+3, 3x+6

The lowest is multiplied by two and four is added: (3x-6)*2+4=6x-8

A number that is two thirds more than the average of the five numbers: (3x-6+3x-3+3x+3x+3+3x+6)/5*2/3=2x

As 6x-8=2x --> **x=2**

The highest of the consecutive numbers: 3x+6=**12**