This is about exercise II.23 in Kashiwara, Schapira; Sheaves on Manifolds. I paraphrase it here:
Let $X=\mathbb{R}^n$ for some $n\geq 1$. Let $k$ be a (commutative) field. Consider the category of $k_X$-sheaves, where $k_X$ is of course the constant sheaf of $k$ on $X$. Prove that a $k_X$-sheaf $P$ is projective if and only if it is zero.
As a hint, they suggest to prove that if $P\neq 0$, it contains a $k_U$ as a direct summand (for some non-empty open $U$), and then go to a contradiciton from here.
It cannot do the first step. I assume the argument has to go like:
If $P\neq 0$, then there is a (wlog connected) open $U$ with $P(U)\neq 0$. Let $s_1,\ldots, s_n$ be a $k_X(U)=k$-basis of $P(U)$ and then embed $k_U$ into $P(U)$ via choosing one of the basis elements. How do I extend this to an embedding of $k_U\hookrightarrow P$ of sheaves on $X$?