How to visually determine the damping ratio when we know the peak amplitude
Is this a mistake in the book or am I not getting something?


No, it's not a (major) mistake in the book. If I plug \$\zeta\$ = 0.24 in the formula, I get \$M_P\$ at  2.146 and, converting to decibels it is 6.63 dB. So not a million miles off 6.5 dB. 

For a second order low pass filter: -