What is that the system to defend the body by producing hormones, including thymosin, which t-cells to mature, and adrenaline, which the body to fight or run away from large external threats?

The correct answer is the immune system, more specifically, the thymus gland. The thymus gland, while it produces hormones like thymosin, it is more closely related to the immune system rather than the endocrine system. This is because lymphocytes that go into the thymus gland mature into T lymphocytes that can either be a helper T cell or a cytotoxic T cell, depending on the stimulus.