Learn Portuguese (Portugal): Ele sugere-te o próximo passo.

The -te is an indirect object pronoun meaning "to you" (informal singular). In European Portuguese, pronouns generally attach to the end of the verb with a hyphen in simple, affirmative sentences like this one.

Why isn't there a word for "to" in the Portuguese sentence, like "sugere a ti"?

The indirect object pronoun -te already has the "to" built into its meaning ("to you"). While you could say sugere a ti if you wanted to put a very strong emphasis on the fact that he suggested it to you (and not someone else), attaching -te to the verb is the standard, everyday way to say it.

Do we ever need to drop letters from the verb when adding an indirect object pronoun like -te?

No! You only drop final consonants (like -r, -s, or -z) when you are attaching a direct object pronoun (like -o or -a). Because -te is an indirect object pronoun, you simply attach it to the conjugated verb sugere exactly as it is.

Why does the adjective próximo come before the noun passo?