= Solution
By the <canonical colimit presentation of a presheaf>, write
$$
P=\operatorname{colim}_{(c,x)\in\int P}H_c
$$
with structure maps $\alpha_{c,x}:H_c\to P$. Since $P$ is a <0-presentable object>, the canonical map
$$
\operatorname{colim}_{(c,x)}\operatorname{Nat}(P,H_c)\longrightarrow\operatorname{Nat}(P,P)
$$
is bijective. Every element of a set-valued <colimit> has a representative in some component. In particular $1_P$ is the image of a transformation $s:P\to H_c$ for some $(c,x)$, so
$$
\alpha_{c,x}s=1_P.
$$
Thus $P$ is a retract of $H_c$. The <representable retract criterion> from part (c), using the assumed <equalisers> in $\mathcal C$, now gives \b[$P$ is <representable>]. Only existence of the representative of $1_P$ is needed; no stronger uniqueness-of-factorization assertion about individual <colimit> injections has been assumed.
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