But: My teacher told me that 13.2 is wrong. I found some dates of when Moon covers Venus and it seems like they happen almost exactly 3 days before and after new Moon. Examples: new Moon - 6. October, covering - 9. October; new Moon - 5. November, covering - 8. November; covering - 28. March, new Moon - 1. April.
So why is my solution wrong?
First of all you are almost there. Your strategy is correct and your answer is close to the right answer.
tl;dr: 13.2°/day angular velocity is not wrong, the number is correct. It's just that it's not the correct number to use in this case. There's one more step you need to add.
I can't emphasize enough how much I disagree with this answer telling you that you should not have asked your question in Stack Exchange.
It's possible that you were not given the explanation why you were wrong as a way to encourage self-research. One of the greatest and most rewarding things is to build the skills for finding things out on our own, either through seeking out alternative sources or (in some cases) experimenting.
We can't experiment on the Moon, so turning to Stack Exchange was a good move. Unfortunately rather than blurt out the answer then tell you you should not have asked, had I been here first I would have left a comment suggesting you sketch the Earth orbiting the Sun and the Moon orbiting the Earth (ignore Venus for the moment) and then draw their positions ~27.3 days later.
The Moon is in the same position relative to the Earth, but now where is the Earth? A comment or two later and you'd have solved it yourself, and then you could have posted an answer to your own question.
Instead you got "Your wrong, here's what's right, and you should not have asked here in the first place. You did something wrong by not insisting your teacher tell you the answer, after all, they're paid for that."
No. A great teacher will inspire you to explore. Welcome to Stack Exchange!
But I digress!
Now, suppose you have your 27.3 day lunar orbital period giving the 13.2°/day angular velocity, and can't go look up anything else, but want to derive a better answer. What can you do?
There are two ways. You can calculate the lunar month from the synodic month (the 27.3 day orbital period) or you can simply subtract the angular velocities!
The Moon does indeed rotate around the Earth at 13.2°/day. No question about it. But the Earth rotates around the Sun at 360/365.2564 = 0.986°/day in the same direction. The difference is 12.2°/day or a period of 29.5 days, which is a lunar month, the average period between new Moons or full Moons.
If all you know is 27.3 and 365 days, you can just use:
$$\frac{1}{T} = \frac{1}{27.3} - \frac{1}{365}$$
To learn more about the difference between synodic and sidereal periods (we have the same distinction for days as well!) see the following:
Because some folks pay so much attention to how the Moon moves in the heavens, there are a surprisingly large number of kinds of months for the Moon! Here's a table from this answer to Is there a timekeeping word for the orbit of a moon?. The first two are the ones discussed above.
kind frame - or - criteria Earth's moon (days)
sidereal inertial wrt stars 27.321661
synodic rotating with Sun-Earth 29.530588
draconitic orbital plane (precesses) 27.212220
(or draconic) time between ascending nodes
(or nodal)
anomalistic time between periapses 27.554551
tropical time between alignments of 27.321582
Moon's axis with the
planet-moon line
