[Steenrod]

My book says that a bulkier nucleophile brings about elimination of halogens in alkyl halides.It cites the example of
$$(CH_3)_3 COH$$ and $$CH_3CH_2COH$$ preferring elimination and substitution respectively. I can compare the two but if I were given only of them and asked which process will they prefer, how do I know?
Thanks.

Edit:My book was talking about the action of the above alcohols on alkyl halides of the form RX.

[discodermolide]

The structure you drew is not an alkyl halide. It may be tert. butanol.
Bulkier nucleophiles are sterically compromised, if they can't undergo displacement they may well act as bases and cause elimination.

[Steenrod]

Sorry for the ambiguity, but my book was talking about the action of the above alcohols on alkyl halides of the form RX(where R is an alkyl group and X is a halogen). I was asking that given any one of them, how do I exactly know what reaction they cause with RX.

[discodermolide]

As I said tertiary butanol is sterically  encumbered and will not displace X from RX.
Ethanol is not sterically encumbered and will displace X from RX. This is a famous named reaction.
So the bulkier the nucleophile the worse it reacts in a displacement reaction, therefore, it will tend to act as a base and cause elimination.