Clarification on LED strip specifications
Interpreting specs such as these found on many marketplace sites can be a bit of an art form, especially when no datasheets are provided.

When in doubt, the best idea is to ask the seller. If they cannot provide the information, then you have two choices: take pot luck, or find another seller!

That being said, here's how I read the information you are being provided in this case:


  
  Input Voltage: Dc 12V – 3A
  


.. is I believe the spec of the power supply that is provided, not the strip itself. In other words, capable of delivering a total of 36W at 12V.


  
  Lamp power: 12V 4.8 Watts
  


.. is most likely per meter i.e. each 60 LEDs. That is a pure guess based typical power requirements and how specs for similar LED strips are presented. You can divide/multiply this out by the actual number of LEDs you plan to use.

If you are planning to power a strip with batteries, the main challenges will be battery life and how many LEDs you have the power to drive. 

Trying to use 2x9V does not seem like a very good idea. While you could probably drive at least a few LEDs with 2x9V, you will be wasting a lot of their already-limited (~500mAh) capacity in the step-down to 12V. And a step-down with resistors is going to be tough to get right. If you cut the strip and can squeeze say 0.5A out of the batteries, that's still 3W to burn off. A voltage regulator would be better if you really must.

AA or even C, D or 6V lantern batteries will be able to drive more LEDs for longer, and you can avoid losses in voltage regulation.