The four major buying behaviors are complex, dissonance-reducing, habitual buying, and variety-seeking buying behaviors. What implications does each of these buying behaviors have for a firm’s promotional strategies?

This question requires each of the 4 major buying behaviours to ideally be listed with reference to the kinds of promotional strategies likely to be employed. You may have quite a few good ideas for strategies that link up with the buying behaviour.
The key is that the question asks for ‘each’ and therefore you should reference all four buying behaviours.

For example:

Cognitive buying behaviour promotional strategies must therefore usually respond with promotion that is information rich (i.e. using print media with long copy).

Dissonance-reducing buying behaviour may involve promotion that confirms the consumer’s choice by showcasing how many others have made the ‘same choice as you’. For example, ‘four our of five dentists agree that Crest toothpaste prevents cavities and whitens teeth’ etc.

Habitual buying behaviour occurs under conditions of low consumer involvement and little significant brand differences. Hence, this is almost pure behavioural decision-making and hence advertising tends to be focused on classical conditioning, in which buyers are taught to identify a certain product by a single symbol repeatedly attached to it.

In variety-seeking situations, the advertising approach differs across firms. Market leaders often want to encourage habituation and therefore employ conditioning strategies, whereas non-incumbent firms rely instead on inducing consumers to switch and instead employ more cognitive approaches and appeal to consumers on the basis of reasons for making the switch.