Potřebuji alespoň dvě možnosti.

Because možnost is a feminine noun.

In Czech, the number two changes form depending on gender:

• dva for masculine nouns
• dvě for feminine and neuter nouns

So:

• dva stoly = two tables
• dvě možnosti = two options
• dvě auta = two cars

Since možnost is feminine, dvě is the correct form.

It is plural because the sentence says two options, not one option.

The basic singular form is možnost.
The plural form is možnosti.

Here it is the direct object of potřebuji, so the phrase is in the accusative. For this noun, the accusative plural looks the same as the nominative plural, so you see možnosti.

A useful pattern to remember:

• after 2, 3, 4, Czech normally uses a plural noun
• after 5 and higher, Czech usually uses the genitive plural

Compare:

• dvě možnosti
• tři možnosti
• čtyři možnosti
• pět možností

Because Czech often leaves out subject pronouns when they are already clear from the verb form.

Potřebuji already means I need. The ending tells you it is 1st person singular, so já is unnecessary.

You could say Já potřebuji alespoň dvě možnosti, but that adds emphasis, something like:

• I need at least two options

Without já, the sentence sounds natural and neutral.

Alespoň means at least.

It is placed before dvě možnosti because it modifies the quantity:

• alespoň dvě možnosti = at least two options

That is the most natural position in this sentence. It tells the listener that two is the minimum acceptable number.

In everyday speech, you may also hear the shorter form aspoň, which means the same thing:

• Potřebuji aspoň dvě možnosti.

Both are possible.

• potřebuji is standard and fully correct
• potřebuju is also very common, especially in everyday spoken Czech

So both of these work:

• Potřebuji alespoň dvě možnosti.
• Potřebuju alespoň dvě možnosti.

The meaning is the same. The first sounds a bit more careful or standard, while the second sounds more conversational.