In guiding my pupil's response to this question, I would first draw attention to the phrasing of the question - 'How far do you agree' as indicative of a well-rounded and considered response - this is not a 'yes' or 'no' question, but encourages both sides of an argument to be explored. I would therefore suggest taking a particular stance to structure the essay overall (focussing on the embarrassment the family cause to Elizabeth), with one or two counterarguments to demonstrate nuanced understanding of the text (one or two points which demonstrate how the family may in fact support Elizabeth, rather than simply embarrassing her). We would work to find a select few scenes of embarrassment within the text to examine in detail, noting any key quotations (particularly those with techniques for close analysis - alliteration, metaphor, simile, repetition, etc) and their effect on the reader, and also consider any wider historical or critical context which would inform our response.
Once this overview of the question and potential examples to include has been established, we would move onto a plan of structuring the essay - 4-5 key points (phrased as topic questions which directly answer the question - 'One way in which the Bennet family are an embarrassment to Elizabeth is...'), each with 3-4 quotations to act as 'evidence' for the points. These quotations must have a purpose beyond merely telling the story - it should be clear how Austen is using them in order to convey something to the reader (here a focus on the effect of literary techniques is important). We would then see where our examples of historical/social and critical context may fit into each point to act as supplementary evidence, and to show the examiner we know the text beyond a surface level. A brief discussion into the key features of a good introduction/conclusion would also be established - introduction to give an overview of the text itself and the overarching argument of the essay (also useful to include some literary context of the text itself here if relevant), while the conclusion sums up the essay and may introduce an original or interesting final point which speaks to the text as a whole.