Here's a short video - with demonstration plus verbal explanations -- that gives clear instructions on how to tie a Half Windsor knot. See the Related Link.
"half the half" is one quarter. One quarter = 1/4 One and a half = 11/2 = 3/2 One quarter of 1 and a half = 1/4 x 3/2 = 3/8 So, half the half of one and a half = three eighths