This follows from the estimate in Theorem 7.9 in Chapter 2 of [@Kollar96]. Namely, for a comb with $m$-teeth, there is a subcomb with $m'$ teeth that is smoothable. And a lower bound of $m'$ is given by $$\label{eq:1}
m' \geq m-(K_X \cdot C_2)+\dim X-\dim_{[f\vert_{C_2}]}Hom({{\mathbb}{P}}^1, X).$$ By assumption, $-(K_X \cdot C_2)+\dim X=\dim_{[f\vert_{C_2}]}Hom({{\mathbb}{P}}^1, X)$. Thus $m'=2$ and the reducible curve is smoothable. If one of the free curves contains a very general point, a very general deformation of this reducible curve will also contain a very general point, thus free.

\[lem:smoothable\] Let $X$ be a Fano $4$-fold of pseudo-index $i(X)$ at least $2$. Let $C=C_1 \cup C_2 \cup C_3$ be a chain of ${{\mathbb}{P}}^1$s and $f: C \to X$ be a stable map. Assume that $-f^*K_X \cdot C_2\leq 3$ and $C_i$ passes through a very general point for $i=1, 3$. Then a general point of any irreducible component of the Kontsevich moduli space containing $(C, f)$ corresponds to an irreducible very free curve.

We first show that every irreducible component of $Hom({{\mathbb}{P}}^1, X)$ at $[C_2]$ has dimension at most $7$. If the deformation of $C_2$ in one component covers the whole $X$, a general point of that irreducible component parametrizes a 