I’m an experienced knitter but haven’t knitted a cable sweater for many years and I’m having trouble understanding the pattern.

There are 4 rows in Panel A, 18 rows in panel B and 8 rows in Panel C. However, the pattern only says to use Row 1 and 2 of the Panels:

1st row: (RS). (P1. Work 1st row Panel Pat A) 0 (1-0-1-0-1) time. P4 (2-2-2-4-
2). Tw2R. P2. (Work 1st row Panel Pat A. P2. Tw2R. P2) 2 (2-3-3-4-4) times.
Work 1st row Panel Pat B. P2. Tw2R. P1.
Work 1st row Panel Pat C. P1. Tw2R. P2.
Work 1st row Panel Pat B. (P2. Tw2R. P2.
Work 1st row Panel Pat A) 2 (2-3-3-4-4) times. P2. Tw2R. P4 (2-2-2-4-2).
(Work 1st row Panel Pat A. P1) 0 (1-0-1-0-1) time.

2nd row: (K1. Work 2nd row Panel Pat A) 0 (1-0-1-0-1) time. K4 (2-2-2-4-2). P2. K2.
(Work 2nd row Panel Pat A. K2. P2. K2) 2 (2-3-3-4-4) times.
Work 2nd row Panel Pat B. K2. P2. K1.
Work 2nd row Panel Pat C. K1. P2. K2.
Work 2nd row Panel Pat B. (K2. P2. K2.
Work 2nd row Panel Pat A) 2 (2-3-3-4-4) times. K2. P2. K4 (2-2-2-4-2).
(Work 2nd row Panel Pat A. K1) 0 (1-0-1-0-1) time.

These 2 rows form pat. Panel pats are now in position.

Cont in established pat, until work from beg measures 17½ (17½-17-17-16½-16½)" [44.5 (44.5-43-43-42-42) cm], ending on a WS row.

How do I work the other rows of the 3 panels into the pattern to make the cable turn out properly?

The instructions for rows 1 and 2 have set the placement of the cable panels, A,B and C. Now you should continue on with row 3 etc. of the cable charts. Since the different panels have a different number of rows and therefore will repeat at different row numbers, you should keep track of the 3 panels separately. Panel A for example will repeat twice in the number of rows that it takes to do Panel C.