Final answer:
The type of long-term memory that Alex demonstrates by knowing details of his birth and first word is explicit memory, specifically a mix of episodic and semantic memory elements.
Step-by-step explanation:
Alex's knowledge of where he was born, the time he was born, and his first word, although not remembered exactly as events, falls under the category of explicit memory. This type of memory includes things that individuals consciously try to remember, recall, and report. More specifically, it's a mix of episodic memory which is about events we have personally experienced, and semantic memory, which is knowledge about words, concepts, and language-based knowledge and facts. Thus, knowing these details about his birth and first word are likely part of Alex's semantic memory because they are facts about his life, whereas if he were to remember specific events and what it felt like to experience those moments, it would be part of his episodic memory.