El ejemplo de mi tutora me hizo comprender que un buen gráfico puede explicar mucho.

Because ejemplo is a masculine noun in Spanish, even though it ends in -o, which is actually the usual masculine ending anyway.

So:

• el ejemplo = the example
• un ejemplo = an example

This is completely normal in Spanish. You just have to learn the gender with the noun.

De mi tutora means of my tutor or more naturally in English, my tutor’s.

Spanish often uses this structure:

• el libro de Ana = Ana’s book
• el ejemplo de mi tutora = my tutor’s example

Spanish can also use possessives like mi, tu, su, but here de mi tutora is used because the thing possessed is el ejemplo, not tutora itself.

So the full noun phrase is:

• El ejemplo de mi tutora = My tutor’s example

Tutora is the feminine form of tutor.

In Spanish, it can mean:

• a tutor
• a mentor
• in some contexts, a teacher responsible for a student group

Here it most likely means female tutor.

Related forms:

• el tutor = male tutor
• la tutora = female tutor

This is the very common Spanish structure:

hacer + infinitive

It means to make someone do something or to cause someone to do something.

So:

• me = me
• hizo = made
• comprender = understand / comprehend

Together:

• me hizo comprender = made me understand

Other examples:

• Me hizo reír = He/She made me laugh
• La película me hizo pensar = The film made me think

Because hizo agrees with the subject, which is el ejemplo de mi tutora.

The subject is:

• El ejemplo de mi tutora = my tutor’s example

So the sentence is literally:

• My tutor’s example made me understand...

Since the subject is he/she/it in English terms, Spanish uses:

• hizo = he/she/it made

Compare:

• Yo hice = I made
• El ejemplo hizo = the example made

Because after hacer, Spanish normally uses an infinitive.

So:

• me hizo comprender = made me understand

Not:

• me hizo comprendí

That would be ungrammatical.

This is the same pattern as:

• me hizo llorar = made me cry
• me hizo cambiar = made me change

In many cases, they mean almost the same thing: to understand.

In this sentence, both would work:

• me hizo comprender
• me hizo entender

A slight tendency is:

• entender = understand
• comprender = understand more fully, grasp deeply

So comprender can sound a little more thoughtful or complete, but in everyday use the two are often interchangeable.

Here que means that.

It introduces a subordinate clause, the thing that was understood:

• me hizo comprender que... = made me understand that...

The clause after que is:

• un buen gráfico puede explicar mucho

So the person understood that a good graph/chart can explain a lot.

In English, that is often optional:

• It made me understand that...
• It made me understand...

In Spanish, que is normally required here.

In Spanish, many adjectives can go before or after the noun, but the position can affect style or nuance.

• un buen gráfico is the normal, natural way to say a good graph/chart
• bueno becomes buen before a singular masculine noun

So:

• un buen libro
• un buen profesor
• un buen gráfico

If you say un gráfico bueno, it sounds less natural here and more contrastive, as if you were distinguishing it from bad ones in a specific situation.

This is a standard Spanish rule.

Bueno shortens to buen before a singular masculine noun:

• un buen día
• un buen amigo
• un buen gráfico

But:

• un libro bueno = if the adjective comes after, it stays bueno
• una buena idea = feminine, so no shortening
• unos buenos gráficos = plural, so no shortening

No, not usually.

Here gráfico means something like:

• graph
• chart
• diagram
• visual representation

So un buen gráfico is a well-made visual aid.

Be careful: English graphic often means vivid or explicit, but Spanish gráfico very often refers to a visual chart or graph.

Because the stress falls on the second-to-last syllable in a way that needs to be marked:

• grá-fi-co

Spanish spelling rules say that words stressed on the third-to-last syllable, like this one, need a written accent.

So:

• gráfico

The accent mark shows the correct pronunciation.

Literally, it means can explain a lot.

Here:

• puede = can / is able to
• explicar = explain
• mucho = a lot

Spanish often uses mucho by itself like this, without adding a noun:

• sabe mucho = knows a lot
• trabaja mucho = works a lot
• explica mucho = explains a lot

So un buen gráfico puede explicar mucho means that a good chart or graph can communicate a large amount of information.

Because the indirect object pronoun me already tells you who is affected.

• me hizo comprender = made me understand

Spanish often uses just the pronoun:

• me, te, le, nos, etc.

You could add a mí for emphasis:

• El ejemplo de mi tutora me hizo comprender a mí que...

But that sounds unnecessary here unless you want strong contrast, like me, specifically.

So the normal version is simply:

• me hizo comprender

Yes. A few natural alternatives are:

• El ejemplo de mi tutora me hizo entender que un buen gráfico puede explicar mucho.
• Gracias al ejemplo de mi tutora, comprendí que un buen gráfico puede explicar mucho.
• El ejemplo de mi tutora me ayudó a comprender que un buen gráfico puede explicar mucho.

These are all slightly different in tone:

• me hizo comprender = made me understand
• comprendí = I understood / I realised
• me ayudó a comprender = helped me understand

The original sentence is perfectly natural and emphasizes the effect of the tutor’s example.