The correct option is
B watch out for
The phrase, 'watch out for' means 'to be careful of something or someone'. In the given sentence, the speaker is asking the listener to be careful of bag snatchers. Hence, this phrase in option B is the correct answer.
The phrase, 'look after' means 'take care of'. Eg: Maddy's grandparents looked after him when his parents travelled out of the city'.
The phrase, 'watch yourself' means: Tobeverycarefulinone'sactionsorspeech,soasnottodoorsaysomethingharmfuloroffensive. Eg: 'Watch yourself when you are near the lake. The water is very deep'.
Given the above meanings, these two phrases are not appropriate to be used in the given sentence. Hence, options A and D are incorrect.
There is no phrase such as, 'see out for'. It conveys no meaning. Hence, option C is incorrect.