'de' is the article used for masculine and feminine nouns, 'het' for neuter words. How to know the difference? Unfortunately the only solution is to know them by heart since there are no tricks whatsoever for foreigners to understand (it's a question of feeling). In this case both 'boek' and 'brood' are neuter words and therefore both have the article 'het'.
I've listened to the recorded voice and the vowel sound in "hij" sounds like the diphthong in the English word "high" but weren't we told that "ij" is pronounced as the mid-high front vowel /e/, that's the vowel sound in the English word "may" (more or less). Or have I misremembered? And how is "ei" in Dutch words pronounced? Help! I feel like giving up!
Hi, 'ij' and 'ei' are usually pronounced the same way in Dutch, that's the fun thing about it. ;)
I think they pronounce it rather like a slightly elongated 'hey', but I'm Flemish myself so it's just an interpretation of the way I hear it. Use Howtopronounce.com, choose your language and type in the word(s) you want to hear. For 'hij' the first version is closer to the way we say it in Flanders, while the second version is more northern in the Netherlands. Same goes for words with 'ei': kei (rock) sounds a little more Flemish, while 'prei' (leek) sounds more Dutch. But overall, you will hear in both versions that 'ei' and 'ij' are pronounced the same.
So hang in there, only perseverance pays off. You will get there. :)