Why Front-to-back ratio compares the main lobe's peak response with the response exactly 180 degrees behind it. On Figure E9-2 the main lobe peak is set on the outer ring, the 0 dB reference, and the small lobe pointing straight down at 180 degrees reaches only the ring 28 dB below that, so the difference is 28 dB. You read the value by counting the dB rings between the two points, not by measuring any physical distance on the paper.
Watch out The choice near 15 dB comes from reading the pattern at 90 degrees off the main lobe, which is the front-to-side ratio, and 3 dB is the half-power level used to find beamwidth, not a lobe ratio.
Front-to-back = straight across the plot, 0 vs 180 degrees. Front-to-side = 90 degrees off.