Learn Portuguese (Portugal): Tenho vinte cêntimos no bolso.

In Portuguese, the verb ending usually tells you who is doing the action. Tenho specifically means "I have" (from the verb ter), so adding the word for "I" (eu) is not necessary unless you want to add emphasis.

Where does the word no come from?

no is a mandatory mash-up (contraction) of the preposition em (in/on/at) and the masculine word for "the" (o). Together, they become no (in the).

The translation says "in my pocket", but doesn't no just mean "in the"?

Yes, literally it says "in the pocket". In Portuguese, it is very common to leave out possessive words like "my" (meu) when talking about body parts, clothing, or personal items. Saying no bolso is the most natural way to express "in my pocket" when it is obvious whose pocket it is.

Is bolso the word for a handbag or purse?

No, bolso specifically means a pocket in your clothing. A handbag or purse is usually called a mala or bolsa. Because bolso and bolsa look and sound so similar, they are a common mix-up for beginners!