Brownian motion hitting time

x is a brownian motion with drift dx=mdt+dz. If x starts from 0, what is the probability that x hits 2 before hitting -4?

If m = 0, then use the martingale Mt = B^2t - t

X=B+mt, B is standar B.M.
Y(t)=exp{cB-c^2 t/2} is a martingale
subsitute B = X-mt in to Y(t)
Y(t)=exp{cX-cmt-c^2 t/2}
Let c=-2m, then Y(t)=exp{cX} = exp{-2mX} is a martingale
Let A be the event that hit 2 before -4
Let B be the event that hit -4 before 2

Let T be the time that either A or B
E[Y(T)] = exp(-2m * 2) * P(A) + exp(-2m * (-4)) * P(B)
E[Y(T)] = E[Y(0)] = 1 (margingale)
also P(A) + P(B) = 1

==> exp(-4m)*P(A) + exp(8m)*(1-P(A)) = 1
P(A) = (exp(8m) - 1) / (exp(8m) - exp(-4m)) given that m != 0