think I can start you off.
In year 1, an equal amount of business was written on 1 March and 1 Sep. Assuming risk spread evenly, then need to work out average exposure date.
Risk written on 1 March exposed for 10 months, say 10 units, risk written on 1 Sep exposed for 4 units - hence 14 units in total. So average exposure period after 7 units, which is mid-Sep (bearing in mind 2 units per month from Sep to Dec).
In year 2 same sort of thing. Business written in year 1 is exposed for the whole year, 24 units (on average 6 months from year end). Business written in Y2, exposed for 14 units (average mid-Sep, 3.5 months from year end as above). So 38 in total. Half is 19 units which I reckon mid-point would be 1 Aug (since 4 units per month Sep-Dec and 3 units in Aug). Bu they seem to have just averaged 6 and 3.5 to get 4.75. No big deal only 8 days out!!!