The first row of element chart represents the primary element of your dragon. These are the primary elements of the defending dragon.
The first column of icons represents how the your primary dragon element deals with another elements.
Second rows tell you that elements will be observers multiple damage (x2), (you can check damage calculator here)
The third rows tell you that elements only get haft damage when under attack your primary elements (first row)
The last rows tell you that elements have no damage when your primary element dragon attacks them.
Keep in mind the dragon city type advantage chart helps you know your enemies and pick the correct dragons for the battle or dragon city mission
You can save the dragon city element chart image to your device to open it quickly.
On more thing. May be this Dragon Rank page interesting for you.
Yes, Dragons can have up to 4 elements, but only the primary element - appearing first in the list - indicates the dragons weaknesses. Each element represents a move type that that dragon can learn. A dragon with 4 elements is ideal as it can learn 4 different element type moves.
Primary elements are the first element a dragon has listed The first element of a dragon indicates which moves it will be weak to The other elements a dragon has indicates the types of moves it can learn!
Some elements are designed to not mix. These are called opposite elements A good example would be Fire an Ice do not breed together.
Some elements have an opposite element which means single element dragons of these types cannot be bred directly. but you can use multi-element dragons to attempt breeding combinations of these elements.
When playing some dragon city events, or even opening your daily calendar. you will eventually receive some Element Tokens which are used to upgrade your habitats past level 2.
The game actually provides you with a good battle chart The battle chart indicates which elements do double damage, and which ones are not very effective This is visible when you click the "Question Mark" icon during battle But here is a copy of that chart!