(Subscript[k, 1]) = 0.01
(Subscript[k, 2]) = 0.01
(Subscript[k, 3]) = 0.5

f[x_, y_, z_, w_] = (Subscript[k, 2])*z - (Subscript[k, 1])*x*y
g[x_, y_, z_, w_] = 
      (Subscript[k, 1])*x*y - ((Subscript[k, 2]) + (Subscript[k, 3]))*z
m[x_, y_, z_, w_] = 
      (Subscript[k, 2])*z + (Subscript[k, 3])*z - (Subscript[k, 1])*x*y
n[x_, y_, z_, w_] = (Subscript[k, 3])*z

f1[x_, y_, z_, w_] = D[f[x, y, z, w], x]
f2[x_, y_, z_, w_] = D[f[x, y, z, w], y]
f3[x_, y_, z_, w_] = D[f[x, y, z, w], z]
f4[x_, y_, z_, w_] = D[f[x, y, z, w], w]

g1[x_, y_, z_, w_] = D[g[x, y, z, w], x]
g2[x_, y_, z_, w_] = D[g[x, y, z, w], y]
g3[x_, y_, z_, w_] = D[g[x, y, z, w], z]
g4[x_, y_, z_, w_] = D[g[x, y, z, w], w]

m1[x_, y_, z_, w_] = D[m[x, y, z, w], x]
m2[x_, y_, z_, w_] = D[m[x, y, z, w], y]
m3[x_, y_, z_, w_] = D[m[x, y, z, w], z]
m4[x_, y_, z_, w_] = D[m[x, y, z, w], w]

n1[x_, y_, z_, w_] = D[n[x, y, z, w], x]
n2[x_, y_, z_, w_] = D[n[x, y, z, w], y]
n3[x_, y_, z_, w_] = D[n[x, y, z, w], z]
n4[x_, y_, z_, w_] = D[n[x, y, z, w], w]

Jaco1=(({{f1[0, 2, 0, 8], f2[0, 2, 0, 8], f3[0, 2, 0, 8], f4[
                0, 2, 0, 8]}, {g1[0, 2, 0, 8], g2[0, 2, 0, 8], g3[0, 2, 0, 8], g4[
                0, 2, 0, 8]}, {m1[0, 2, 0, 8], m2[0, 2, 0, 8], m3[0, 2, 0, 8], m4[
                0, 2, 0, 8]}, {n1[0, 2, 0, 8], n2[0, 2, 0, 8], n3[0, 2, 0, 8], n4[
                0, 2, 0, 8]}}))

Eigenvalues[Jaco1]

Jaco2=(({{f1[20, 0, 0, 80], f2[20, 0, 0, 80], f3[20, 0, 0, 
                80], f4[20, 0, 0, 80]}, {g1[20, 0, 0, 80], g2[20, 0, 0, 80], g3[20, 0, 0, 
                80], g4[20, 0, 0, 80]}, {m1[20, 0, 0, 80], m2[20, 0, 0, 80], m3[20, 0, 0, 
                80], m4[20, 0, 0, 80]}, {n1[20, 0, 0, 80], n2[20, 0, 0, 80], n3[20, 0, 0, 
                80], n4[20, 0, 0, 80]}}))

Eigenvalues[Jaco2]