You need to consider the movement as a whole, and apply the worst case.
That is to say, if the LH element moves through Good Going only, it can move up to 4 BW.
If it moves through Rough or Bad Going at any point of the movement, even for a tiny bit, it can only move 1BW in total, including any Good Going portion of the movement.
In your case, that means that the LH element has to stop short of entering Bad Going, as entering would reduce its movement distance to 1 BW, which is incompatible with the 2 BW it has just moved to get there. What it can do is move up to 4 BW through Good Going, stop right at the edge of the Bad Going terrain, and then in the next turn move 1 BW into it.
The relevant wording can be found in page 9, in the Tactical Move Distances table:
"4 BW If Light Horse [...] and only in good going
1 BW If any troops other than [...] and in bad or rough going for any part of the move [...]"
So, rule of thumb: if you are moving through Rough or Bad Going at all, use the reduced distance.
Note also that moving along a road is an exception, and units that follow the road for their entire movement use their Good Going distance even if the road is crossing Rough or Bad Going (page 6, last paragraph).
Hello Bertandspm (your English is quite good by the way).
The answer you seek is in “Tactical Move Distances”, page 9 paragraph 2:- “1 BW if any troops other than fast foot, Auxilia or Warband and in bad or rough going for any part of the move...”
However, “Fleeing”, page 12 paragraph 7 says:- “(Fleeing) stops before completing its move and lines up if its front-edge (or front corner) contacts (e) for troops other than Psiloi or Light Horse, any bad going except marsh it is not already at least partly in.”
So all troops flee at full speed and are not slowed by marshes, and Psiloi and Light Horse flee through all bad going at full speed and are not slowed. (But note that rough going is not mentioned... ...which probably means that no fleeing troops are slowed by rough, but only by bad going...other than marshes)
Remember, movement is a voluntary move action that costs PIPs, while fleeing is an involuntary combat outcome.