how the information of "claims notified in accident year" should be utilised? in another word, how to understand the numbers settled is bigger than number notified? and, as a result, can't understand the underlying rationale of the corresponding solution, i.e. the triangle of ACPC settled, in the bottom of page 95, would appreciate your advice.

The claims notified in the accident year, isn't actually used in the solution. It was a "red herring" so to speak. it is simply telling you how many claims were notified (ie reported) in the original accident year. So for the 2015 accident year, 300 claims were notified during 2015 of which 230 were settled in 2015. In 2016 a further 130 claims from the 2015 accident year were settled, some of these may have been notified in 2015 (and were therefore part of the original 300) and some may have been notified in 2016 (and were therefore not part of the original 300) and so on. The triangle at the bottom of page 95 is obtained by dividing the inflated incremental payments in each period (ie the first triangle on page 94) by the corresponding number of claims settled in each period (as provided in the question). So for 2015 we have 139,000/230 followed by 93,000/130 and so on. This triangle gives us the inflation adjusted (ie all in 2018 terms) average settled claim amount in each development period.