Is 4 ethyl-2,4 octadiene a correct name? How can i identify if it's incorrect or correct?

It looks ok to me. Draw out the 2,5 octadiene part, tack on the ethyl group on carbon 4, then count the longest chain. It is 8. Counting the ethyl group carbons it is 6 one way and 7 the other which doesn't alter the initial name of octa for 8.