In the solution, 3u --> 4p is used because we have already used units ('u') in the ratio at the beginning 8:5:6 to increase Tang by 1.5 times (from 6units to 9units). We also, know that Yeo and Lim gave to Tang in the ratio of 3:1 - total of 4 units. But hold on, we just used units already above, so not to confuse the "two different units", we use parts in the second situation (total of 4 parts is given to Tang). So an increase of 3units of Tang is because of the 4parts from Yeo and Lim.
We need to do this because 1) we do not wish to confuse the units in the first ratio with the units in the second ratio 2) 4 (parts) does not nicely divide into 3 (units). By doing this, it is clear that we need to use common multiples to change the ratio at first (8:5:6) to (32:20:24) so that the increase of 12units in Tang is a result of the 4parts from Yeo and Lim. Thus 9units from Yeo and 3units from Lim.