6. A five-digit number $\overline{a b c d e}$ satisfies
$$
ac>d, dd, b>e
$$
(for example, 37201, 45412), if its digits change with the position in a manner similar to the monotonicity of a sine function over one period, then this five-digit number is said to conform to the "sine rule". Therefore, there are $\qquad$ five-digit numbers that conform to the sine rule.
6.2892 .

From the problem, we know that $b$ and $d$ are the maximum and minimum numbers among $a, b, c, d, e$. It is easy to see that $2 \leqslant b-d \leqslant 9$.

Let $b-d=k$. In this case, there are $10-k$ ways to choose $(b, d)$, and $a, c, e$ each have $k-1$ ways to be chosen, i.e., $(a, c, e)$ has $(k-1)^{3}$ groups. Therefore, there are $(k-1)^{3}(10-k)$ numbers that conform to the sine rule.
Thus, the total number of numbers that conform to the sine rule is
$$
\sum_{k=2}^{9}(k-1)^{3}(10-k)=2892 \text { (numbers). }
$$