The absolute value of a number is the distance the number is from zero. Thus |6-2x| is the distance between 6-2x and the origin. If this distance is less than 4 then 6-2x is between -4 and 4. That is,
Thus x satisfies two conditions, first
Now solve each of the two inequalities separately and remember that for x to satisfy |6-2x|<4 it must solve both of the inequalities -4 < 6-2x and 6-2x < 4.