Mathematica is calculating the characteristic polynomial according to the common convention:

CharacteristicPolynomial[{{-6,4,-8},{28,-15,32},{21,-12,25}},x]

(* 2-5 x+4 x^2-x^3 *)

m={{-6,4,-8},{28,-15,32},{21,-12,25}};

Det[m-IdentityMatrix[3]x]

(* 2-5 x+4 x^2-x^3 *)

It may be that your book is always adjusting the polynomial such that the sign on the highest power is positive, by multiplying by -1 as needed. There is no harm in this, since the usual use of the polynomial is to solve for its roots, which are not changed by doing this,

Best regards,

David

Sorry, Ilian. We were working together!

Edit: I think Ilian's answer more likely, that the book is using a different convention. In any case, you can be comfortable multiplying by -1, as the roots are unchanged.