There's an interesting asymmetry in the Shock Superiority Chart. Look at RC vs LC: attack superior. But LC vs RC is not defense superior! Combined with the Numidians TQ advantage over the Roman cavalry, there's plenty of incentive to get attacking. And that MA of 9 means no enemy is going to OW before them, either.
With these facts in mind, Tychaeus decides to attack the sole Roman cavalry
unit on the Roman left. He hopes to quickly rout that unit, then turn on the
flanks of the Roman infantry using momentum.
Movement: The Numidian's 9 MPs give them just enough movement to get on the flank of the RC. As with Hannibal, Tychaeus's initiative is high enough that it doesn't really matter whether he uses a line command or individual orders; either way, both cavalry units can move. Note that Tychaeus has a Command Restriction word ("Num Cav") and hence can't give orders/line commands to any units other than Numidian Cavalry [4.29]. So he can't, for example, order the nearby slinger unit to fire.
Missile Fire: There is no Reaction Fire from the Roman Cavalry, as they have no missiles. But the Numidians fire their javelins as part of their movement. They need a 3 or less to hit (Mounted Javelins at range 1 need a 4 to hit, with a +1 drm for moving). They roll '8' and '0', so one LC is Missile Low, and the other scores a cohesion hit on the RC.
Leader Casualties: Since there is a leader in the target hex, and the missile attack rolled a '0', the Romans must check for a leader casualty [8.19]. The subsequent dr is 4, no effect (another '0' is needed to score a casualty).
Shock Markers: As light units, the LC units don't have to be given a SHOCK Check TQ marker, but then they couldn't shock attack [7.25B]. So the Carthaginian marks them to check TQ.
Shock: Resolving the shock, the LC units and their target check TQ. The Numidians are safe with rolls of '4' and '0', but the Romans roll an '8' and so take 3 more cohesion hits, for a total of 4.
Since leaders are involved in the Shock, they must check for leader casualties [4.53]. Neither leader rolls a '0', so both are safe.
Consulting the Clash of Spears & Swords Chart, LC attacking RC in the flank yields a basic shock column of 7. This column is adjusted by the relative sizes of the combatants, 4+4=8 attacker vs 3 defender. Since at least one attacker moved, this ratio is rounded up to a 3:1 [8.36 TWO], meaning shift two columns to the right. This give a final column of 9.
The attacker is automatically superior since it's a flank attack, so the defenders cohesion hits will be doubled.
Each leader can modify the shock dieroll by using his charisma [8.36 THREE]. Since both leaders have a charisma of '1', they cancel out and there is no dieroll modifier.
The Carthaginians roll a '7', which yields a 2(3) result, modified to a 2(6)
by attack superiority. Each LC takes a hit, while the defending RC is now
up to 10 cohesion hits. Since 10 exceeds the RC's TQ of '6', the RC routs
[8.37]. It moves two hexes towards its retreat edge [10.31]. Since the
attacking force included cavalry, that cavalry must pursue [10.41].
Pursuit: Tychaeus decides to have the unit without a leader pursue, as he himself wants to remain on map for further momentum phases. Consulting the Cavalry Pursuit Table, he rolls a '3', adds 1 for Numidian LC, which results in a Break Off. The routed RC undergoes Rout Movement, moving its full MPs towards its retreat edge.
On a "real" map, the edges are usually farther away from the front lines, but here the cavalry runs off the edge of the map and is eliminated [10.33]. The LC unit must advance, and is now finished [10.42(1)].
Note that Prefect Falco accompanies the routing unit for the first two hexes, but doesn't go along with the subsequent rout move (because he doesn't to be eliminated for leaving the board [10.33]). It's his choice as to whether to accompany the routed unit or not [10.38].
Momentum: Tychaeus now can try for Momentum, and succeeds in doing so by rolling a '3'.
Now the Romans can Trump, in the same manner that Tychaeus trumped Antonius. The only eligible (equal or better initiative, not Finished) Roman leader is Flamininus; he attempts to trump and rolls a '9', which fails. Flamininus is now Finished [5.44], and will not get to activate at all!
Tychaeus now proceeds to his first Momentum Attempt.