You may only construct structures/wonder stages if you can produce the required resources in their cost, or your adjacent opponents have the missing resources you require (and you have the coins necessary to purchase those goods).
The rules are probably not as specific as they should be, but you can glean the correct answer by looking at the examples given. Unless a structure is free, you must have the resouces to build it and/or the coins necessary to buy the resources from your neighbors.
Some cards have a resource cost. To construct them, the player must produce the corresponding resources AND/OR buy them from one of his or her two neighboring cities.
The rules then give an example of the Giza board, its current production, and the fact that it cannot build the Aquaduct.
The resources of a city are produced by its Wonder board, its brown cards, its gray cards, and some yellow cards. To build a structure, a player’s city must produce the resources indicated on its card. Example : Giza produces 2 Stones, 1 Clay, 1 Ore, 1 Papyrus and 1 Textile :
- its player cannot build the Aqueduct (cost : 3 Stones) as his city only produces two of the three stones required by that structure.
It is clear that since Giza requires 3 Stone to build the Aquaduct and cannot build it, but it would be quite odd if its neighbor's could buy 3 stone from Giza and build it themselves. This is further driven home buy the split '/' resource icon explanation on the last page of the Quick Rules or the regular rules tells you that only one of the pictured resources is available to you and your neighboring cities, not both. As well as the double resource icon providing two of the pictured resource.
the card produces one of the two pictured raw resources each turn.
Clarification : the player can use one OR the other resource to build a structure (or a wonder phase) but NOT both in a given turn. Neighboring players may purchase either, regardless of what the owner chooses to produce.
And finally, the last 2 Stone example from the rules, showing that both neighboring cities can buy her 2 stones and she can also use the same 2 stones in the same turn. This indicates that the resources a city has a available is the maximum that they can produce, and that both neighbors can buy 0, 1, or 2 stone the same turn the that the city owner uses 0, 1, or 2 stone.
Example B: during a game turn, both neighboring cities buy from her 2 Stones for a total of 8 coins (2 per resource). In the same turn, she can build a Library (cost : 2 Stones + 1 Textile) thanks to her resources, even though she has sold them to her neighboring cities.