Learn Hardcore Spanish (Spain): Gracias; es mejor que guardes el papel sellado en la cartera. - Thanks; it’s better that you keep the stamped paper in your wallet.

guardar (infinitive) → guardes (present subjunctive, tú form)
guardas would be indicative (stating a fact: you keep) and sounds wrong here. You can use an infinitive, but the structure changes:
Es mejor guardar el papel... = It’s better to keep the paper... (more general, not directly addressing “you” as strongly)
Es mejor que guardes el papel... = It’s better that you keep the paper... (direct advice to the listener)

What form is guardes exactly, and who is being addressed?

Guardes is the present subjunctive of guardar for tú (informal singular you). The subject pronoun tú is omitted because Spanish usually drops subject pronouns unless needed for emphasis or clarity.

Could I replace guardes with an imperative like guarda?

Yes, but the tone changes:

Es mejor que guardes... = softer, more advisory (it’s better that you...)
Guarda el papel sellado en la cartera. = more direct command (Keep the stamped paper in your wallet.) Spanish often uses es mejor que + subjunctive to sound polite or indirect.

Why is there que after es mejor?

In Spanish, when es mejor introduces a recommendation about someone doing an action, it commonly uses que + subjunctive:

Es mejor que + (subjunctive verb)
This is a standard pattern for advice and evaluations (similar to It’s better that...).

What does guardar mean here—save, keep, store, or put away?

Here guardar means to keep/put away safely (to store or keep in a safe place).
It’s not the computer sense of save unless the context is digital. With papel and cartera, it strongly suggests keep it stored safely.

What exactly is el papel sellado?

El papel sellado literally means the stamped/sealed paper.

papel = paper/document (often a physical document)
sellado = stamped or sealed (having an official stamp/seal) It’s sellado because it agrees with papel (masculine singular).

Why is the adjective after the noun: papel sellado instead of sellado papel?

In Spanish, descriptive adjectives normally come after the noun:

papel sellado = stamped paper
Putting it before (sellado papel) is generally unnatural, and would only happen in special stylistic cases (and even then, it’s not common with sellado).

What does cartera mean in Spain—wallet or handbag?

In Spain, cartera commonly means wallet (especially a men’s wallet) and can also mean briefcase/portfolio depending on context.
If you specifically mean a woman’s handbag, Spanish from Spain more often uses bolso.
If you mean a small “coin purse” style wallet, you might hear monedero.

Why use en la cartera and not a la cartera?

Because the idea is location/containment: the document ends up in the wallet.

en la cartera = in the wallet
a would suggest direction toward a place in a different way, but with guardar you normally use en for where you store something.

Is the semicolon in Gracias; es mejor que... normal?

It’s correct but slightly formal. In everyday writing you’d often see:

Gracias. Es mejor que guardes... (two sentences), or
Gracias, es mejor que guardes... (comma, if it’s one flow) The semicolon neatly separates two closely related statements.

Why is Gracias used instead of Muchas gracias?

Gracias is the neutral, common Thanks.
Muchas gracias is simply stronger/more emphatic (Thanks a lot / Thank you very much). Both work; it depends on tone.

Could this be made more formal (using usted)?

Yes. You’d change the verb to the usted subjunctive form:

Es mejor que guarde el papel sellado en la cartera.
Here guarde is present subjunctive for usted (formal singular you).