Good Kata for what it wants to do. Minor suggestions for the description:

• Your job is to write a class 'Walker()'

  Just write 'Walker', maybe emphasize it.

• This class should have a couple of methods:

  "This class should have two methods:". This is a specification, let's be precise :)

The following list could use some clean-up: Why precede each method with a number? There should be 2 list items, one for each method, with the description below at matching indentation.

• walk(string):

  a method that takes a string of directions for Mr. Strolly to walk as input (this hasn't happened yet, why past tense?)

• coords():

  a method that returns Mr. Strolly's position relative to his house*

* Instead of pre-populating the __init__ method, you could specify that Mr. Strolly's initial position is his house at (0,0).