One thing that might help is to know some of the language around maths:
"of" almost always means "multiply (times)"
So if you are finding half of something, that means half times something, and if you have done multiplying fractions, then you could do it like that (as in the example your teacher sent). To multiply fractions, you just multiply the tops and the bottoms of your fractions.
That would be quite a hard way of doing it at this stage of understanding fractions, though - they are probably more wanting you to get an idea of what quarters and eighths look like, and how they relate to each other, and what equivalent fractions are, rather than having to do written calculations on them.
If you haven't done multiplying fractions, I think the visual methods are easier. Mark your 3/4 point on a number line, as people have shown. You can then see where the half way point is on the number line. Because it is halfway between the 1/4 and the 2/4, you are going to have to divide the number line into more than four bits. If you divide the whole space equally into eight bits instead of four, then your 3/4 mark will show you that it is the same as 6/8. That's quite an important thing to understand, as it shows you what equivalent fractions are - the same amount can be written as 3/4 or 6/8.
Having eight pieces will make your 'halfway point' fall exactly on one of the dividing lines, rather than in between. Then you can see that your half way point is three of those bits. The line is split into eight equal pieces, so each piece is an eighth, and you have three of them, so three-eighths (which is 3/8; or also the same as saying 3 out of 8).