Learn Portuguese (Portugal): As mãos dele estão sujas.

While many words ending in -ão change their ending (like limão to limões or cão to cães), mão is one of the exceptions that simply adds an s to become mãos. Other common words that follow this "just add s" rule are irmão (brother, becoming irmãos) and cidadão (citizen, becoming cidadãos).

Why is it As mãos and not Os mãos? Doesn't the "o" at the end mean it's masculine?

Normally, words ending in -o are masculine, but mão is a classic exception. It is a feminine noun. Because of this, everything connected to it in the sentence must also be feminine: the plural article As and the plural adjective sujas (instead of sujos).

Why do we use estão instead of são for "are"?

We use estão (from the verb estar) because being dirty is a temporary state. His hands are dirty right now, but they will be clean once he washes them! The verb ser (which would be são) is used for permanent characteristics.

Could I say As suas mãos instead of for "his hands"?