You are correct. You deal 8d6 + ability mod damage if both attacks hit
Let's go through how we get there:
On a crit, you double all of the dice you would have rolled, including sneak attack, then add the relevant modifier
This is clearly defined in the basic rules (page 75), and in the PHB under the section for critical hits (emphasis mine):
For example, if you score a critical hit with a dagger,
roll 2d4 for the damage, rather than 1d4, and then add
your relevant ability modifier. If the attack involves other
damage dice, such as from the rogue’s Sneak Attack
feature, you roll those dice twice as well.
So, your shortsword attack with sneak attack would normally be 1d6 (shortsword) + 2d6 (sneak attack) or 3d6 damage. On a critical hit you double the number of dice: so (2*3)d6 = 6d6 plus the relevant ability modifier.
Attacking with an off hand shortsword is a separate attack, but can still crit
Assuming that your off hand attack hits, it would be a crit (the creature is still surprised, so the assassinate feature still applies). It deals (2*1)d6 or 2d6 damage. You don't add any non-negative modifiers to off-hand attacks. You also don't reapply sneak attack, since that feature can only be used once per turn.
Putting that together, you get 6d6 + ability modifier + 2d6 = 8d6 + ability modifier damage.