\[\boxed{\text{854\ (854).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
\[C_{x}^{4} = 14 \cdot C_{x - 2}^{2},\ \ x > 0;\]
\[\frac{x!}{(x - 4)!} = \frac{14 \cdot (x - 2)!}{(x - 2 - 3)!}\]
\[\frac{(x - 1) \cdot x}{(x - 4)} = \frac{14}{1}\]
\[14x - 56 = x^{2} - x\]
\[x^{2} - 15x + 56 = 0\]
\[D = 225 - 224 = 1\]
\[x_{1} = \frac{15 - 1}{2} = 7,\ \ \]
\[x_{2} = \frac{15 + 1}{2} = 8.\]
\[Ответ:7\ или\ 8.\]