intimate
Never intimate intimate details to strangers.
The sentence advises against subtly hinting at private personal information when speaking with strangers.

Meanings
to imply or hint at something subtly rather than state it directly
- She intimated that changes were coming.
- His tone intimated displeasure without saying so.
closely personal, private, or detailed
- They had an intimate conversation by the fire.
- Intimate details should not appear in public emails.
Word origin
Both senses come from Latin intimus ('innermost'), the superlative of intus ('within'). The adjective sense (private, personal, innermost) developed first; the verb sense ('to imply, suggest indirectly') came from a Late Latin verb intimāre meaning 'to make known' — the metaphor being that you're conveying something from your innermost thoughts.
Fun fact
The verb 'intimate' (/ˈɪntɪmeɪt/) and the adjective 'intimate' (/ˈɪntɪmət/) follow the same /eɪt/-vs-/ət/ pattern as 'separate', 'moderate', 'appropriate', 'estimate', 'graduate', and 'duplicate'. In each pair, the verb ends in a clear /eɪt/, the adjective or noun in a reduced schwa — a signal that quietly tells you the part of speech.