For this one, I took advantage of the ability to rotate vectors to get the job done. I am confused about the use of the bracket indexing though, and I do not quite understand why I needed to use ⊃ and ⊂ as much as I did.
∇R←PEEIGHTEEN M;F;N;BEST;⎕IO ⎕IO←1
⍝ Find the greatest total through a triangle M
⊣⎕FX 'R←X BEST Y' 'R←(X+Y)⌈1⌽Y+-1⌽X'