Question 265287
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Suppose the two digit numbers are "10A+B" and "10C+D:, then

(10A+B)(10C+D) = (10B+A)(10D+C)

That simplifies to

AC = BD

so the reason 32 x 46 = 23 x 64 is because the product of the tens digits
of 32 and 46 (3x4 equals the product of the units digits 2x6).

All the possibilities are below:

1.  21 × 24 = 504 and 12 × 42 = 504
2.  21 × 36 = 756 and 12 × 63 = 756
3.  21 × 48 = 1008 and 12 × 84 = 1008
4.  31 × 26 = 806 and 13 × 62 = 806
5.  31 × 39 = 1209 and 13 × 93 = 1209
6.  32 × 46 = 1472 and 23 × 64 = 1472
7.  32 × 69 = 2208 and 23 × 96 = 2208
8.  41 × 28 = 1148 and 14 × 82 = 1148
9.  42 × 12 = 504 and 24 × 21 = 504
10.  42 × 36 = 1512 and 24 × 63 = 1512
11.  42 × 48 = 2016 and 24 × 84 = 2016
12.  43 × 68 = 2924 and 34 × 86 = 2924
13.  62 × 13 = 806 and 26 × 31 = 806
14.  62 × 39 = 2418 and 26 × 93 = 2418
15.  63 × 12 = 756 and 36 × 21 = 756
16.  63 × 24 = 1512 and 36 × 42 = 1512
17.  63 × 48 = 3024 and 36 × 84 = 3024
18.  64 × 23 = 1472 and 46 × 32 = 1472
19.  64 × 69 = 4416 and 46 × 96 = 4416
20.  82 × 14 = 1148 and 28 × 41 = 1148
21.  84 × 12 = 1008 and 48 × 21 = 1008
22.  84 × 24 = 2016 and 48 × 42 = 2016
23.  84 × 36 = 3024 and 48 × 63 = 3024
24.  86 × 34 = 2924 and 68 × 43 = 2924
25.  93 × 13 = 1209 and 39 × 31 = 1209
26.  93 × 26 = 2418 and 39 × 62 = 2418
27.  96 × 23 = 2208 and 69 × 32 = 2208
28.  96 × 46 = 4416 and 69 × 64 = 4416

Edwin</pre>