Simplify substitute or you can write the charachteristic equation:

k^2-k-2=0

Thus, k=2,-1

Thus, the set

C_1*e^{2t}+C_2*e^{-t} is the basis for the solutions.

Again, charachterstic equation,find the values of m for which y=e^mt is a solution of d^2y/dt^2+dy/dt -6y=0.

k^2+k-6=0

Thus,

k=-3,2

Thus,

e^{-3t} and e^{2t} are solutions,

Thus possible values of "m" are,

-3,2