Learn Danish: Uden tillid kan vi ikke stole på hinanden. - Without trust, we cannot trust each other.

In Danish, when a verb requires a preposition, like stole på (to trust or rely on), the reciprocal pronoun hinanden (each other) acts as the object of that preposition. So 'trust each other' is expressed literally as 'trust on each other': stole på hinanden.

Why does the sentence say kan vi instead of vi kan?

This is due to the V2 (verb-second) rule. Because the sentence starts with the prepositional phrase Uden tillid (Without trust), the first verb kan must take the second position in the sentence. This forces the subject vi to switch places with the verb.

Is the word stole related to the English word 'stole' (the past tense of steal)?

No, this is a classic false friend! The Danish verb at stole means 'to trust' or 'to rely on' (almost always used with the preposition på). If you wanted to talk about stealing, you would use the verb at stjæle.

Why are there two completely different words for 'trust' (tillid and stole) in this sentence?

They are different parts of speech. Tillid is the noun for 'trust' or 'confidence' (used here in 'Without trust'). Stole is the verb for the action of trusting (used here in 'we cannot trust'). English uses the exact same word for both, but Danish requires different words depending on whether it is a thing or an action.