The structure יש לך את זה or in general, יש למישהו את המשהו is probably foreign to Hebrew and doesn't fit in very well, it's very difficult to explain. It's like a mix of Hebrew and English grammar that migrated into the languages and became a fixed expression. But it is rather common.
I agree with Dmitry that זה is not a direct object in this sentence, but BartiBar's point that זה "is functioning" as accusative is interesting. My current and very limited take-away is that את זה is idiomatic even though it's not a direct object and that the stress is probably on its definiteness (את isn't used with an indefinite object). Since BartiBar is a moderator, I have to assume that he knows how the sentence is routinely said. Now more than ever I want to get a copy Muraoka's Modern Hebrew, where he shows how modern Hebrew differs from "classical" Hebrew. I bring this point up because in classical Hebrew יש never is followed by את. For instance, רות ג יב (Ruth 3:12): וגם יש גואל קרוב ממני. In my limited understanding of Mishnaic and rabbinic Hebrew, I cannot say for sure that יש never has את, but it would certainly appear to be unique to modern Hebrew in the history of the Hebrew language to use את with יש and so Dmitry has a good point that we should look to the influence of other languages here. Poking around the internet, יש את זה is clearly idiomatic, as this advertisement indicates: https://milled.com/castro.il/final-sale-00cAqA_hxyzMZMjC
Ok this one is easier: "But Coach Joe, i can't do it, i don't know where to find the courage to face it!" Coach Joe leans in: "יש לך את זה בתוכך." Or that one co-worker... "Jenny, you've been humming Christmas carols since Thanksgiving." "Oh! It's just that Christmas Spirit!" אני יודעת, יש לך את זה בתוכך" Rolls eyes...
You can find the words individually on Memrise in the Memrise for Duolingo course and in another Memrise course. There's also ANKI Duolingo vocab pack.
Once you know the individual words they don't sound as quick, it's something that happens to all new language learners [we all think it sounds too quick even though the average speed across all languages is pretty similar - even sign language].
The Memrise for Duolingo course uses the same voice, but individual words. The other course is just an Israeli guy who made a course. They are both awesome (I use them both daily - each lesson is less than 5 min.). The Israeli does speak slower and his course includes both single words and sentences.
Links are below. (Note these are courses made by users not official Memrise courses so you have to go to the Memrise website initially to sign up, then you can use the app.)
Hebrew Duolingo on Memrise! http://www.memrise.com/course/1031737/
I'm learning Modern Hebrew Complete (with audio) on Memrise! http://www.memrise.com/course/364795
The anki Duolingo course is from the Facebook group: 'Hebrew Duolingo learners'. You can get the link there or search the anki website.
I hope this is helpful. 18 January 2019