According to Piaget when children reach the point of being able to generalize and engage in mental trial and error by thinking up hypothesis and testing them in their heads they are in :

The correct option is Formal operational stage.

Explanation:

According to Jean Piaget's theory of cognitive development, children progress through four distinct stages:

1. Sensorimotor Stage (Birth to 2 years): Infants learn about the world through their senses and motor activities.

2. Pre-operational Stage (2 to 7 years): Children begin to use language and symbolic thought, but their thinking is still egocentric and intuitive rather than logical.

3. Concrete Operational Stage (7 to 11 years): Children gain the abilities of logical thought concerning concrete (hands-on) events and objects.

4. Formal Operational Stage (12 years and above): In this stage, individuals develop the capacity for abstract thinking, hypothetical-deductive reasoning, and systematic problem-solving. They can form hypotheses, engage in mental trial and error, test these hypotheses internally, and generalize concepts beyond concrete situations.

Therefore, when children reach the point where they can think hypothetically and test ideas in their heads, they have reached the Formal operational stage.