12. Given an integer $k$ satisfying $1819<k<2019$, and making the solution of the system of linear equations in two variables $\left\{\begin{array}{l}4 x-5 y=6 \\ 5 x+4 y=k\end{array}\right.$

all integers, then the number of $k$ that satisfies the condition is $\qquad$.
$5$