Use the binomial theorem to find the 18th term in the binomial expansion of [2p-r(sqrt(2)]^27

=-2211521495040 sqrt(2) p^10 r^17

It counts the 18th term from P^27 in desceding order. P^27, p^26, p^25...........18th.

how did you get that?

The coefficient is arrived at by: 27C17 x 2^18=2211521495040. The rest is simple expansion of the 18th term by binomial expansion.