No me aprietes la mano tan fuerte.

Because this is a negative command addressed to tú.

In Spanish:

• Affirmative tú command: aprieta
• Negative tú command: no aprietes

So:

• Aprieta la mano. = squeeze the hand
• No aprietes la mano. = don’t squeeze the hand

Negative commands for tú use the present subjunctive, which is why you get aprietes.

Because apretar is a stem-changing verb: e → ie in stressed forms.

You can see that in forms like:

• aprieto
• aprientas
• apriete
• aprietes

Since no aprietes is built from the present subjunctive, the stem change appears there too.

So it is not apretes, but aprietes.

Me is the indirect object pronoun, meaning something like to me or for me.

Literally, Spanish structures this more like:

• Don’t squeeze me the hand

But in natural English, we say:

• Don’t squeeze my hand

Spanish often uses an indirect object pronoun with body parts to show who is affected.

Because Spanish normally uses:

• an indirect object pronoun (me)
• plus the definite article (la)

with body parts.

So instead of saying my hand, Spanish usually says the hand, while me already tells you whose hand it is.

That is why No me aprietes la mano sounds more natural than No aprietes mi mano in most situations.

Because mano is an exception: it is a feminine noun even though it ends in -o.

So you say:

• la mano
• una mano
• mi mano derecha

This is just something you need to memorize. Mano is one of the most common exceptions to the usual -o = masculine pattern.

Tan fuerte means so hard / that hard, while muy fuerte means very hard.

In this sentence, tan fuerte suggests the pressure is more than it should be:

• No me aprietes la mano tan fuerte. = Don’t squeeze my hand so hard.

You could say muy fuerte in some contexts, but tan fuerte is more natural when reacting to someone’s excessive force.

Here, fuerte is functioning adverbially: it describes how someone is squeezing.

So even though fuerte is often taught as an adjective meaning strong, in sentences like this it means something like:

• hard
• strongly

Spanish often uses adjective forms this way after verbs.

Because Spanish usually omits subject pronouns when they are not needed.

The verb form aprietes already tells you the speaker is talking to tú, so tú is unnecessary.

You could say:

• Tú no me aprietes la mano tan fuerte

but that would add emphasis, contrast, or emotional force. Normally, No me aprietes la mano tan fuerte is enough.

Because with negative commands, object pronouns go before the verb.

So:

• No me aprietes la mano.

But with an affirmative command, the pronoun is attached to the end:

• Apriétame la mano.

Notice the written accent in apriétame. It is added to keep the original stress.

Yes, it is grammatically possible, but it sounds less natural in ordinary Spanish.

Native speakers usually prefer:

• No me aprietes la mano tan fuerte

because Spanish commonly expresses possession of body parts through:

• the pronoun (me)
• plus the article (la)

Using mi mano is more likely if you want special emphasis on my hand, not someone else’s.

Yes. That is also very natural.

There is a small nuance:

• tan fuerte focuses on how hard
• tanto focuses on how much / to such a degree

In many real situations, both would sound perfectly normal:

• No me aprietes la mano tan fuerte.
• No me aprietes tanto la mano.

In Spain, with vosotros, you would say:

• No me apretéis la mano tan fuerte.

That is the negative vosotros command, and like other negative commands, it also uses the subjunctive form.

So:

• tú: No me aprietes...
• vosotros: No me apretéis...