Final answer:
The correct word to complete the sentence is 'embark,' which means to begin a significant journey or adventure.
Step-by-step explanation:
The correct answer to the question, 'I am about to ___ on a long and dangerous adventure.' is option A. embark. To embark means to begin a journey, especially on a ship or airplane, but it can also metaphorically mean to start a new venture or adventure. Options B, C, and D do not appropriately complete the sentence in this context. 'Encroach' refers to gradually and stealthily taking over space or rights, often without permission. 'Endeavor' is an attempt to achieve a goal, and 'endure' means to suffer something difficult or painful patiently. Embark is the most fitting word for someone about to start an adventure.