When we are learning a new language we pay attention to things that native speakers don't necessarily pay attention to. They don't have to. But we do! That is how we learn.
Here's a case in point. A learner was watching a Yabla video about numbers. When do we use ordinal numbers, and when do we use cardinal numbers? In the video in question, Marika is talking about dates. Every language expresses dates a bit differently, and there are often different options. The basic premise is that in contrast to how we do it in English, Italians mostly use a cardinal number (not an ordinal number as in English) when talking about a specific date, preceded by the definite article.
The learner's question was, "Is there some special reason why Marika uses the preposition di (of) when talking about August, but not for the other dates?" It's a great question, and it is exactly the kind of question we like learners to ask. Because native speakers, or even experienced non-native speakers, might not be aware they are saying di (of). They just know it sounds right without thinking about it and may or not be able to explain why.
Si dice il cinque aprile, il quattro luglio,
One says the fifth of April, the fourth of July,
il nove maggio, ehm, il venti di agosto.
the ninth of May, uhm, the twentieth of August.
Captions 24-25, Marika spiega - Numeri Cardinali e OrdinaliPlay Caption
So the short answer is that when talking about a specific date, you can just say the cardinal number (with the definite article before it) followed by the month. There was nothing special about the month of August to cause Marika to use the preposition di. She might have used it because it was the last month she said in a series and it just sounded better to her. And it's a valid option. So it is not wrong to use the preposition, but more often than not, Italians don't use it.
Let's look at another example. Antonio is telling us about a festival in August, in his area of Italy. In the following example, he just says the cardinal number and the month. He is talking about a specific date.
E poi il diciotto agosto
And then on the eighteenth of August
la statua rientra qui nel... ehm, nel santuario.
the statue returns here, in the... uh, in the sanctuary.
Captions 19-20, Antonio - al SantuarioPlay Caption
In the same video, a few captions earlier, he is again talking about the dates of the festival. He uses the preposition di in the first instance.
Ehm, la Madonna della Grotta è la protettrice di Praia a Mare
Um, the Madonna of the Cave is the patron saint of Praia a Mare
e viene fatta una festa il quattordici e quindici d'agosto.
and there is a feast on the fourteenth and fifteenth of August.
Per l'esattezza inizia il quattordici a mezzanotte
To be exact it starts on the fourteenth at midnight
e finisce il diciotto agosto di ogni anno.
and ends on the eighteenth of August every year.
Captions 13-16, Antonio - al SantuarioPlay Caption
When he cited two dates together he used the preposition di before agosto. Sometimes it just seems clearer to add it. It could also be that since agosto starts with a vowel and diciotto ends with a vowel, it's easier to put a consonant in the middle, so it's clearer and easier to say.
Marika, in this video about the news, doesn't add the preposition (febbraio starts with a consonant!).
Il ventiquattro e venticinque febbraio,
On the twenty-fourth and twenty-fifth of February,
in Italia si terranno le elezioni politiche,
Italy will hold political elections
che decreteranno la scelta di un nuovo governo.
that will ratify the choice of a new government.
Captions 8-9, Anna e Marika - in TG Yabla Italia e MeteoPlay Caption
The important thing to know is that it is correct to leave out that preposition and that we generally use a cardinal number except for when it's the first. When it's the first of the month, we use the ordinal number primo (first).
E si dice: il primo luglio, il primo agosto,
And one says: the first of July, the first of August,
il primo settembre.
the first of September.
Caption 28, Marika spiega - Numeri Cardinali e OrdinaliPlay Caption
And if we are talking about the first few days of a month, we can say it like this with the plural of primo (note we use the preposition di (of)):
I primi di gennaio (the first days of January)
I mesi che ci interessano sono quelli di metà marzo, aprile,
The months that interest us here are half of March, April,
maggio e i primi di giugno.
May, and the first [days] of June.
Captions 29-30, Adriano - Le stagioni dell'annoPlay Caption
It's funny this question has come up about the preposition di, because in our previous lesson we also talked about the preposition di and how it is common to use it when talking about saying "yes" and "no." In that case, too, it's an option. Learning which option works better comes with a lot of listening and repeating, and keeping your eyes and ears open. We thank the learner who wrote in about this topic!
Di is one of those prepositions that most learners of Italian struggle with, so don't feel bad if you often get it wrong. You are not alone! Non sei solo/sola!