this is a carrot זה גזר, it starts with זה=this is. this carrot הגזר הזה, first is a noun הגזר, second is הזה. You have to repeat it till you remember it. It is the same with all the other words. this is a woman זאת אישה, this woman האישה הזאת, this is a table זה שולחן, this table השולחן הזה etc...
Yea, ה is as a definite article the. if it is without ה , it is a word with an indefinite article. גזר a carrot, הגזר the carrot. https://www.duolingo.com/skill/he/Introduction-to-adjectives/tips-and-notes, https://www.duolingo.com/skill/he/Letters-1/tips-and-notes, https://www.duolingo.com/skill/he/Determiners/tips-and-notes. Read tips and notes, articles and this, that is explained there.
This is a common confusion. In both languages we can convey the same concept with different emphasis or shades of meaning by using different words, grammar, or word order. Note the difference in grammar: the subject of "This carrot..." is "carrot"; the subject of "This is..." is "This".
For the Hebrew forms, see the Tips for the "Adj. Intro" skill on the Duolingo website. Study everything under the "Summary of Simple Phrase Structures" heading.
Also, here's a link to the notes for many of the course skills on one web page: