Whats the difference between 毁灭，销毁，和烧毁？
毁灭 is the general term for 'to destroy' 

销毁 also means destroy, but it is more specific. 


To 销毁 something, you have to have possession of it. If you delete the data in your computer, you can claim it is 销毁数据 (or 毁灭数据), but if you hack in someone else's computer and delete data there, you can only say you are 毁灭数据.
To 销毁 something, you have to have legitimate right to do it. Destroying the opium in China's standpoint was a legal act of 销毁違法商品 (destroy illegal goods); but in the British's eyes. it was an act of 非法毁灭私有財物 (illegal destruction of private property)
To 销毁 something, that something must have physical form. You cannot 销毁 a dream, an ideal or a reputation. 
销毁 has to be a human's act. We can say a natural fire  毁灭了一万棵树 (destroyed ten thousand trees) , but not 销毁了一万棵树


You can 毁灭 something that you do not have possession of. The object doesn't need to have physical form, for example: ideal, dream or enemy, and the act need not to be legal; Of course you can also legal or legally destroy (毁灭) physical things like city or building

烧毁 is the verb 烧(to burn) plus its result complement 毁 (destroy), it means "burn and destroy" or "destroy with fire"