It seems simple to me. There are six possibilities for the "arrangement" of the pancakes.
B/G G/B - B/B B/B - G/G G/G

The Brown/Gold cake can be positioned with either color up (the first two)
The Brown/Brown cake can be positioned with either Brown side up (the second two) and
The Gold/Gold cake likewise can be positioned with either Gold side up (the third two)

One out of three initial choices will be Brown, and if so, of the three possibilities. two of them
are Brown on the bottom side..

So, the 2/3 answer is correct.