(C) $-\dfrac{9}{4}$
Here $a = k$, $b = -6$, $c = -4$. For equal roots, $b^2 - 4ac = 0$:
$$(-6)^2 - 4(k)(-4) = 0 \implies 36 + 16k = 0 \implies k = -\frac{9}{4}$$
Source: Chapter 4, Section 4.4 Nature of Roots
For equal roots, the discriminant $b^2 - 4ac = 0$. Substituting the coefficients and solving gives $k = -\dfrac{9}{4}$. Note that $k \neq 0$ (otherwise it wouldn't be a quadratic equation), and this value satisfies that condition.