The measure of one of two complementary angles is 6 degrees less than one half the measure of the other. find the measure of the smaller angle

It's helpful to choose letters to represent the measures of these complementary angles.  Let x represent one and y the other.

What does "complementary angle" mean?  x + y = ??

Let x be the smaller angle.  First, we take "half the measure of the larger angle," or (y/2).  Then we subtract 6 degrees from this result (y/2).  The result is the xmaller angle, x.

Now you have two equations in x and y.  Solve for one of these angles, and then find the other.  Please show your work.