After a couple of years, it’s a little tired to refer to 6e as an abomination. But whatevs.
The info you’re looking for starts on p. 111 of the Seattle core rule book. In short:
Attacker desires to injure someone on the other side of a barrier. The target has to use a Minor action to gain the DR benefit of Cover status, but you make your normal AR vs DR comparison.
Attacker makes an attack test. Before applying net hits, subtract half the structure from the weapon’s damage. From here it can take a little bit of interpreting: if it were me, damage reduced to 0 by the barrier means the bullet was not able to penetrate all the way through. Do not pass go, do not collect 200¥. One could feasibly rule that 0 still allows net hits to be applied and force a soak roll. YMMV.
If there is still a positive number after the reduction, apply net hits to damage and the target has to soak.
Heavier weapons (and APDS or exploding ammo) applies to base damage, giving things like Roomsweepers extra punch to break through.
Does that help?