PREMISE: Increased frequency of SERIOUS crimes committed by local teenagers.
PREMISE: City introduced "curfews" to keep teenagers at home at night.
PREMISE: Most crimes committed by local teens occur between 3pm and 6pm.
CONCLUSION: Curfew unlikely to reduce SERIOUS crimes committed by local teens.
Aside: I added SERIOUS, because we're told that citizens are worried about the increase in SERIOUS crimes.

Now check the answer choice, while reminding ourselves about the conclusion.

(A) Similar measures adopted in other place have failed to reduce the number of teenagers in the late evening
Does this weaken the conclusion that the curfew is unlikely to reduce SERIOUS crimes committed by local teens.?
No. This premise actually STRENGTHENS the author's conclusion by suggesting that the curfew will be largely ignored.
ELIMINATE A

(B) Crimes committed by teenagers in afternoon are mostly small thefts and inconsequential vandalism
Does this weaken the conclusion that the curfew is unlikely to reduce SERIOUS crimes committed by local teens.?
YES!
If most afternoon teen crimes are NOT serious, then it's quite possible the SERIOUS crimes committed by teens occur at night, in which case the curfew just may help to reduce SERIOUS crimes.
KEEP B

(C) Teenagers are much less likely to commit serious crimes when they are at home than when they are not at home
Does this weaken the conclusion that the curfew is unlikely to reduce SERIOUS crimes committed by local teens.?
NO.
As it stands (when we ignore answer choice B), it SOUNDS like most crimes (serious and non-serious) occur from 3 - 6pm. So, any kind of late-night curfew will have no effect on crime.
ELIMINATE C.

(D) Any decrease in the need for police patrols in late evening would not mean that there could be more intensive patrolling in the afternoon
Does this weaken the conclusion that the curfew is unlikely to reduce SERIOUS crimes committed by local teens.?
NO. The conclusion is all about whether the teen CURFEW will reduce crime.
ELIMINATE D.

(E) The schools in Parktown have introduced a number of after school programs that will be available to teenagers until 6pm on weekday afternoons
Does this weaken the conclusion that the curfew is unlikely to reduce SERIOUS crimes committed by local teens.?
NO. The conclusion is all about whether the teen CURFEW will reduce crime.
ELIMINATE E

Answer: B