Learn Farsi: خانه‌ی من از بانک دورتر است اما پارک نزدیک‌تر است. - My house is further than the bank, but the park is closer.

You add the suffix -tar to the end of a regular adjective. In this sentence, dur (far) becomes durtar (further), and nazdik (close) becomes nazdiktar (closer).

I know az usually means "from". Does it mean "than" here?

Yes! When used with a comparative adjective (one ending in -tar), az translates to "than". Notice the order: you put az before the thing you are comparing to (az bank), followed by the adjective (durtar).

Why is the word order az bank durtar ast instead of durtar az bank ast?

In Farsi, the "than" phrase (az bank) usually comes before the comparative adjective (durtar). And because Farsi places verbs at the end of the sentence, the "is" (ast) is placed at the very end. Literally, it translates to "from the bank further is".

Why does khane have a -ye attached to it?

This is the connector called ezafe, which links a noun to its owner. Because khane (house) ends in a silent 'h' acting as a vowel, it takes the -ye form instead of just -e to connect smoothly to man (I/me), making khane-ye man (my house).