Counting shortest paths on a triangular grid
Jelly, 7 bytes

;IAṀc$Ṁ


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How?

;IAṀc$Ṁ - Link: list of two integers   e.g. [-4, -9]
 I      - incremental differences           [-5]           (since -9 - -4 = -5)
;       - concatenate                       [-4, -9, -5]
  A     - absolute values                   [4, 9, 5]
     $  - last two links as a monad:
   Ṁ    -   maximum                         9
    c   -   choose (vectorises)             [126, 1, 126]  (9c4=9c5=126 and 9c9=1)
      Ṁ - maximum                           126