Let's divide 9246 crowns among 4 people in the following way: If $A$ gets $2 K$, then $B$ gets $3 K$, if $B$ gets $5 K$, then $C$ gets $6 K$, and if $C$ gets $3 K$, then $D$ gets $4 K$.
According to the task, if $A$ receives $10K$, then $B$ receives $15K$, $C$ receives $18K$, and $D$ receives $24K$. Therefore, $9246K$ must be divided into four parts in the ratio $10:15:18:24$. If $A$ receives $10xK$, then

$$
10x + 15x + 18x + 24x = 9246
$$

from which

$$
x = 138
$$

Thus, $A$ receives $1380K$, $B$ receives $2070K$, $C$ receives $2484K$, and $D$ receives $3312K$.

(László Szántó, Pécs.)

Number of solutions: 35.