Learn Italian: Anna ha sei cani.

No, numbers from two to ten do not change to match the gender of the noun they describe. Whether you are counting masculine words like cani (dogs) or feminine words like gatte (female cats), it stays sei. Only the number one (uno or una) changes depending on the word's gender.

How do you pronounce ha, and why are we using it here?

ha is the "he/she/it" form of the verb avere (to have), which we use here because we are talking about Anna (she). In Italian, the letter "h" is completely silent, so ha is pronounced exactly like a short "ah".

The singular word for dog is cane. Why does its plural end in -i?

Cane belongs to a group of Italian nouns that end in -e in the singular. Nouns in this group can be masculine or feminine, but they all share the exact same rule for the plural: the -e at the end always changes to an -i. That is why one dog is un cane and six dogs are sei cani.

Do I need to put a word for "the" before sei cani?

Not in this sentence. Just like in English, you simply say the number and the noun (sei cani) when you are stating a general quantity. You would only add a word for "the" (like i) if you wanted to say "Anna has the six dogs" to talk about a specific group of dogs you already mentioned.