Pragmatic language impairments
The essay will be about pragmatic language impairments. In particular as a result of damage to the RIGHT hemisphere (NOT the LEFT hemisphere).
You can certainly start off in the Introduction by mentioning the theory of lateralisation (that is how right and left hemisphere have supposedly different functions).
You can also explain that there is a lot of research about language impairments when the left hemisphere is damaged (the left hemisphere is considered the site of language), but there is not as much about RIGHT hemisphere which is the focus of the essay.
Explain the role of the right hemisphere with regards to pragmatic functions. Remember that this is an essay for a module in Neurolinguistics.
Therefore, the focus has to be on the linguistic aspect, anything that is related to language (ignore things like difficulty in understanding people’s facial expressions or changes in behaviour due to right hemisphere damage).
Analyse the effects on different aspects of language such as,
Speech acts (a threat, joke, promise).
Register (may be overly informal).
Initiating, terminating, turn-taking in conversational exchanges.
Providing sufficient information for communicative intention (relevance).
Adequate or appropriate prosody/tone.
Coherence of discourse topic, maintenance and shift
The idea of the essay is to analyse how damage to the right hemisphere can have an impact on language and cause pragmatic impairments.