For equal roots, discriminant must be zero. Equation: kx^2 - 2kx + 6 = 0. Discriminant: (-2k)^2 - 4(k)(6) = 4k^2 - 24k = 0. Factor: 4k(k - 6) = 0, giving k = 0 or k = 6. Option B only gives k=6 (incomplete), Option C gives incorrect values, and Option D is wrong since valid solutions exist.