78. $\overline{a b c d}$ is a four-digit number, its reverse number is $\overline{d c b a}$, if $2 \overline{a b c d}=9 \overline{d c b a}$, try to find all $\overline{a b c d}$ that satisfy the condition.
Answer: 8991 or 8181
Solution: From $2 \overline{a b c d}=9 \overline{d c b a}$, we can deduce that $a$ must be an even number,

So the maximum value of $a$ is $8, 2 \overline{a b c d}<18000$.
If $d \geqslant 2$, then $9 \overline{d c b a} \geqslant 18000$ which leads to a contradiction,

Therefore,
$$
d=1,
$$

Thus,
the unit digit of $2 d$ is 2,

which means
the unit digit of $9 a$ is 2,

So
$$
a=8 .
$$

Hence, the four-digit number is $\overline{8 b c 1}$,

Then
$$
2 \times \overline{8 b c 1}=9 \times \overline{1 c b 8},
$$

That is
$$
2 \times(8001+100 b+10 c)=9 \times(1008+100 c+10 b),
$$

Simplifying, we get
$$
8 c-b=63,
$$
(1) When $c=9$, $b=9, \overline{a b c d}$ is 8991.
(2) When $c=8$, $b=1, \overline{a b c d}$ is 8181.
Therefore,
$\overline{a b c d}$ is 8991 or 8181.