requesting, entrusting with, pretend, hint
托 centers on placing something in another's care or using a gesture to convey an indirect message: entrusting a task, making a request, or hinting at something without stating it outright. The 'pretend' sense extends this idea to putting on a false appearance as a kind of indirect communication.
托 combines 扌 (hand) with 乇, which likely contributes the sound and may suggest the idea of placing or supporting something. The exact origin of 乇 is uncertain, but the character is used for entrusting or requesting via a hand gesture.
The hand radical 扌 beside 乇 looks like a hand holding something out to another person. Picture someone extending a hand to entrust a message or hint at a request.
For タク, imagine entrusting a tack to someone: you hand them a thumbtack and say 'tack' as a hint to hang something up. Tack -> タク.
sharing one's lot with another; being in the same boat
religious mendicancy; asking for alms; monk's begging
brood parasitism (planting one's eggs in another bird's nest, as demonstrated by the cuckoo, etc.)
saucer (for a teacup)
stipule
mendicant orders
mendicant priest
intraspecific brood parasitism
interspecific brood parasitism
receptacle; torus
teacup saucer