Other way using function:
Clear["`*"];
b = 2;
k[a_] := Maximize[{-x^2*a - 3*x*b + 1, -(6/8) <= x <= -(4/8)},
x]; Map[k, {1, 2, 3}]
Function with Do:
Clear["`*"];
b = 2;
f[z_] := (Do[
k = Maximize[{-x^2*a - 3*x*b + 1, -(6/8) <= x <= -(4/8)},
x], {a, {z}}]; k);
Map[f, {1, 2, 3}]