In the WotC article it creates the "Favored Soul" origin for Sorcerers and it gives it the Extra Attack feature at level 6. Say I then multiclassed into Ranger to get its Extra Attack at level 5. Would they stack so I could get 3 or 4 attacks in a turn?
No. This is addressed in the PHB (Pg 164, Extra Attack). The only class that can expand the ability of Extra Attack to make more than 2 attacks per attack action is the Fighter. The rules for stacking Extra Attack as they relate to non-fighters and fighters is in the multiclass section of the PHB.
PHB, page 164:
If you gain the Extra Attack class feature from more than one class, the features don't add together. You can't make more than two attacks with this feature unless it says you do (as the fighter's version of Extra Attack does). Similarly, the warlock's eldritch invocation Thirsting Blade doesn't give you additional attacks if you also have Extra Attack.
Regardless of gaining it at level 5 or 6, any class feature that gives you multiple attacks on your attack action does not stack with another class feature with the same or similar effect. Fighter is currently the only route to go to have 3 or 4 attacks solely on the attack action.