They are all correct. There is very little difference between 'hold on' and 'hang on' in this context. 'Hang on' suggests more effort (perhaps because of greater speed), but either could be used in this situation. Likewise, 'tight' or 'tightly' are both possible. 'Tight' is a flat adverb - like 'hard' or 'fast' - so it is correct to say "hold/hang on tight". In some cases, a flat adverb and its 'ly' counterpart have different meanings ( e.g. 'hard' and 'hardly'), but in this case they don't: 'tight' and 'tightly' are both used to mean the same thing. The only thing wrong with the sentence is the choice of verb 'dash off', which is very unnatural :people dash, but vehicles cannot. If you're working from a book written by someone who thinks that buses can 'dash off', I wouldn't necessarily trust it.

Sorry, I don't agree with Lan's answer. Correct: He HELD ON TIGHTLY to the handrails. "To hold" is the correct verb to describe that he has his hands tightly on the handrails e.g. to avoid falling down the stairs. "Tightly" is an adverb, so describes a verb. To explain the others: >> "held on tight" Technically NOT correct, as "tight" is an adjective (describes a noun) not an adverb (describes a verb). HOWEVER it is very common that Americans do not use adverbs in speech! This is a key difference between US and British English. My understanding is that this is not strictly "correct" and not recommended for written English, even in the US. (To my British ears, it sounds wrong.) However, languages evolve, and one day, this will probably become accepted as correct. You can read more about this here: https://www.chronicle.com/blogs/linguafranca/2017/07/17/the-americans-have-no-adverbs/ Some other common examples that Americans SAY: "He ran real quick" (should be "he ran really quickly") "It works great" (should be "it works well") >> "hung on tightly" This makes grammatical sense, but sounds odd. "to hang" means something is suspended / dangling. e.g. "the picture hung on the wall" (the picture is not really trying to hold on to the nail on the wall) To me, "hang/hung" is more of a passive activity, and therefore it sounds odd to say "tightly", which implies some active effort. More likely adverbs are, for example: "the picture hung crookedly on the wall", "the picture hung proudly on the wall" etc So "he HUNG ON TIGHT to the handrails" sounds a bit like he is dangling beneath the handrail, his feet in the air, and this doesn't make a lot of sense. (Unless, he already fell over the handrails...) >> hung on tight As above, this depends whether you accept the mixing of adverbs and adjectives Finally, the (American) idiom is "Hang tight" https://www.merriam-webster

adverb?

2 things 1. HANG ON TIGHT and HOLD ON TIGHT are both IDIOMS But they have a different although similar meaning. a) HANG ON TIGHT means (hold with your hands for dear life :P...) b) HOLD ON TIGHT (means wait here! while I get back usually - so to wait in one place) 2) And as for TIGHT or TIGHTLY actually both are technically correct, and tightly is more grammatically correct because it is an adverb. However, because this is an IDIOM (means it's just how the sentence is used) the correct answer is: a) hung on tight