At first let's have a look at Donald Benge's rules:
"Each catapult may shoot one shot per turn to hit any enemy piece or pieces that are one adjacent space away connected by a road or sea-lane. On the game board, some spaces are marked with a small yellow slot that point to non-connecting spaces that can also be hit by catapults. A catapult may also shoot at any piece in an adjacent field that is not completely obstructed by mountains.... A catapult may board a galleon and shoot at any enemy vessel one connected space away or at any land piece that is on a space that targets the galleon with a yellow slot...."
Since mountains are not really recognizable on the board it's obvious to skip this remark within the rules.
The essential of the rules:
1.A catapult shot hits a piece or pieces on a directly (by a road or sea-lane) connected adjacent space.
2. The following pairs of unconnected spaces are marked with yellow slots so that catapult shots are bidirectionally possible here:
a) 2-player-board
South
140 / 142 (land spaces)
148 / 149 (land spaces)
175 / 176 (land spaces)
141 / 706 (land / sea space)
171 / 703 (land / sea space)
158 / 512 (land / sea space)
North
240 / 242 (land spaces)
248 / 249 (land spaces)
275 / 276 (land spaces)
241 / 806 (land / sea space)
271 / 803 (land / sea space)
258 / 508 (land / sea space)
3. If a catapult is standing on a space with three steps a camel or knight can be hit on the connected adjacent field.
4. Catapult shots are bidirectionally possible between a seaport and the connected sea space marked with an anchor.
A catapult at the seaport could either commandeer an unoccupied enemy galleon (without regeneration) or dump the galleon by a shot.
Supplement:
On the southern island there are two fields which are situated between pairs of unconnected spaces marked with yellow slots:
Field A27 between space 140 and space 142,
field A22 between space 148 and space 149
Because there is only one field of the northern island which is situated between a pair of unconnected spaces marked with yellow slots,
field B33 between space 240 and space 242,
catapult shots starting from the above-mentioned spaces towards the fields A27, A22 and B33 are prohibited for the sake of fairness.