Haec medicina mihi prorsus non placet.

Because placēre works differently from English to like.

In Latin, placēre means to be pleasing to someone. So the person who experiences the liking goes into the dative case.

• mihi = to me
• medicina = the medicine
• placet = is pleasing

So Haec medicina mihi placet literally means:

This medicine is pleasing to me.

That is how Latin expresses I like this medicine.

Because the subject of the sentence is haec medicina, not I.

• placet = it pleases / is pleasing
• placeo = I please

In this sentence, the medicine is the thing doing the pleasing, so the verb must agree with medicina, which is third person singular.

So:

• haec medicina ... placet = this medicine ... pleases
• not placeo, which would mean I please

Haec is nominative feminine singular here.

It agrees with medicina, which is also:

• feminine
• singular
• nominative

So:

• haec medicina = this medicine

Latin demonstratives must agree with the noun they describe in gender, number, and case.

A quick comparison:

• hic = masculine nominative singular
• haec = feminine nominative singular
• hoc = neuter nominative singular

Because medicina is feminine, Latin uses haec.

We know from both case and verb agreement.

medicina is in the nominative singular, which is the normal case for the subject. The verb placet is also singular, agreeing with it.

So the structure is:

• haec medicina = subject
• mihi = indirect object / dative of reference
• non placet = is not pleasing

So literally:

This medicine is absolutely not pleasing to me.

Prorsus means something like:

• completely
• absolutely
• entirely
• quite

With non, it strengthens the negation:

• prorsus non placet = does not please at all
• or absolutely does not please

So the sentence has stronger force than a simple mihi non placet.

Because they do different jobs.

• non simply negates the verb: does not please
• prorsus adds emphasis: absolutely / completely

So:

• mihi non placet = I don’t like it
• mihi prorsus non placet = I absolutely don’t like it / I really don’t like it at all

Latin word order is much more flexible than English word order, because case endings show the grammatical roles.

So Haec medicina mihi prorsus non placet could be rearranged in several ways without changing the basic meaning.

This order is natural and clear:

• Haec medicina first: introduces the thing being talked about
• mihi next: shows who is affected
• prorsus non placet at the end: gives the key statement, with emphasis on the dislike

Latin often puts the verb near the end, and emphasis can affect placement.

The most straightforward translation is this medicine, but medicina can sometimes mean more broadly:

• medicine
• remedy
• treatment
• medical treatment

So the exact English wording depends on context. But grammatically, haec medicina simply means this medicine / this remedy.

A very literal translation is:

This medicine is absolutely not pleasing to me.

A more natural English translation is:

I really don’t like this medicine.

Or, with the emphasis of prorsus:

I don’t like this medicine at all.

Yes, but it is not exactly the same in tone.

• haec medicina mihi non placet = this medicine does not please me
• ego hanc medicinam non amo = I do not love/like this medicine

With things like food, plans, books, or medicine, Latin often prefers placēre for the idea of liking.

Also notice the grammar changes:

• with placet, the thing liked is the subject: haec medicina
• with amo, the thing liked becomes the direct object: hanc medicinam

So both are possible, but placet is especially common for this kind of statement.

Because non normally negates the word or phrase that follows, and in sentences like this it usually comes before the verb.

So:

• non placet = is not pleasing

That is the standard Latin way to negate the verb.
The adverb prorsus is inserted before non placet to intensify the negation:

• prorsus non placet = absolutely does not please

Sometimes yes, if the context already makes it obvious who is meant. Latin often omits things that can be understood from context.

But here mihi is useful because placet by itself only means is pleasing. The dative tells us to whom it is pleasing or not pleasing.

So in this sentence, mihi makes the meaning explicit:

This medicine is absolutely not pleasing to me.