The program is essentially 2 counters. The first counter controls the low die, when it reaches the maximum it will trigger a count on the high counter.
    1 0000:                        org     0
    2 0000: f8 f0                  ldi     0f0h      ; setup temporary storage
    3 0002: a2                     plo     r2
    4 0003: 90                     ghi     r0
    5 0004: b2                     phi     r2
    6 0005: f8 11                  ldi     011h      ; Both dice start at 1
    7 0007: a7                     plo     r7
    8 0008: e2                     sex     r2
    9 0009: 17          loop:      inc     r7        ; increment low die
   10 000a: 87                     glo     r7
   11 000b: fa 0f                  ani     0fh       ; strip high die for compare
   12 000d: 73                     stxd
   13 000e: 6c                     inp     4         ; read switches
   14 000f: fa 0f                  ani     0fh       ; keep only low switches
   15 0011: 60                     irx
   16 0012: f7                     sm                ; see if die is greater than switches
   17 0013: 33 2a                  bdf     good1     ; jump if not
   18 0015: 87                     glo     r7        ; get the high die value
   19 0016: fa f0                  ani     0f0h      ; strip low die value
   20 0018: fc 10                  adi     010h      ; increment high die
   21 001a: 73                     stxd
   22 001b: 6c                     inp     4         ; read switches
   23 001c: fa f0                  ani     0f0h      ; keep only high switches
   24 001e: 60                     irx
   25 001f: f7                     sm                ; see if die is greater than switches
   26 0020: 33 26                  bdf     good2     ; jump if not
   27 0022: f8 11                  ldi     011h      ; reset both dice to 1s
   28 0024: 30 29                  br      save      ; and save result
   29 0026: f0          good2:     ldx               ; recover high die value
   30 0027: f9 01                  ori     1         ; set low die value to 1
   31 0029: a7          save:      plo     r7        ; save result
   32 002a: 3f 09       good1:     bn4     loop      ; see if IN is pressed
   33 002c: 87                     glo     r7        ; if so, then display dice on data displays
   34 002d: 52                     str     r2
   35 002e: 64                     out     4
   36 002f: 22                     dec     r2
   37 0030: 30 09                  br      loop