Option A: The phrase 'to walk' expresses a purpose. The given sentence does not require a purpose. The phrase does not complete the sentence in meaning. Hence option A is incorrect.
Option B: The verb 'walk' does not express any action in the given sentence. It needs to be conjugated in relation to the subject 'She'. Hence B is incorrect.
Options C and D: We use the preposition 'by' (by foot) when referring to a mode of travel 'by plane', 'by car', etc.
But we talk about going somewhere walking, we use the expression 'on foot' and not 'by foot'. It's a set phrase and is used most commonly. 'by foot' sounds odd when used.
Hence option C is incorrect and D is the correct option.