Please help me, i don't understand this at all :(

I don’t know how much this will help as i don’t know the specific methods used in your lesson, but what i personally do is break down the number as much as i can.

32 can be simplified to 2^5. this is the fourth root, so you take out four of the 2’s to the outside by the 6. therefore it becomes 6(2) which = 12 along with the other 2 and an x left inside the fourth root “house”. btw i would write it out but doesn’t let me attach pictures for some reason, and i don’t have the symbols on my keyboard. ):

we now simplify 512 in the second term. 512 is the same thing as 32 times 16, which is 2^9. we take out four of the 2’s, leaving us with 2^5. we can take four more 2’s out, leaving us with a 2 and an x in the inside of the fourth root “house”. on the outside we have 2 2’s, leaving us with a product of 4.

third term. 16 can be simplified to 4^2, or 2^4. we can take all four of them out since it’s the fourth root. there are also four x’s, so we take them out, leaving us with 2x. there isn’t anything left in the “house”.

now, we go from left to right. to better illustrate it, i will use “{ }” as the fourth root.

12 {2x} - 4 {2x} + 2x

8 {2x} + 2x . that’s as simplified as it can get. hopefully this helps! ):