How do you write it correctly: "v techenie" or "v techenii"?

**The rule is simple: "v techenie" is a preposition, "v techenii" is a noun with a preposition.**

If you can replace the phrase with "za vremya" (for the duration) or "v period" (during the period), then you write "v techenie" (without the I at the end). Examples: "v techenie dnya" (during the day), "v techenie goda" (during the year), "v techenie vsego soveschaniya" (throughout the entire meeting). Here we're talking about a period of time, a time interval.

"V techenii" is only used when you're talking about the literal flow of something - a river, a liquid, events as a process. For example: "v techenii reki byli porogi" (there were rapids in the river's current) or "v techenii vremeni proizoshli izmeneniya" (changes occurred in the flow of time - though this second one sounds a bit odd and is rarely used). Essentially, it's the noun "techenie" (flow) in the prepositional case, and you can replace it with "v hode" (in the course of) or simply remove part of the phrase without losing meaning: "v hode reki byli porogi" (in the course of the river there were rapids).

In practice, almost all modern texts about time use "v techenie." And "v techenii" is rare and mostly appears in descriptions of physical processes. If you're unsure - go with "v techenie," and you'll be right 99% of the time 😊