Question

What are the two processes used by producers to obtain energy

Answer 1

Answer;
The two processes used by producers to obtain energy are photosynthesis and chemosynthesis.

Explanation; 
Producers are those organisms that can make their own energy in an ecosystem using biochemical processes. These biochemical processes are photosynthesis and chemosynthesis.
Photosynthesis involves use of energy from the sunlight together with water and oxygen to make simple sugars. The process converts solar energy to chemical energy (simple sugars). 
Chemosynthesis involves use of chemicals as the energy source, rather than sunlight , to make simple sugars such as glucose. 
Glucose from both processes is then used for respiration to generate energy or stored in form of starch. 

Answer 2

The answer to this question would be : chemosynthesis and photosynthesis

The word photo from photosynthesis means light. In photosynthesis, the producer is making carbohydrate using the sunlight.
In chemosynthesis, the producer is making the carbohydrate without light. This reaction only happens in dark condition.