I. Politicians have promised to ........ the goal of eradicating extreme poverty many times but have failed because they cannot agree about what exactly counts as poverty and how exactly to measure it.
II. Reserve Bank hoped that a cut in its benchmark rate will .......... a reduction in inflation and improve confidence in the economy.

In the context of given statements 'achieve' is most gramatically appropriate. Achieve means to beget usually an objective, goal or an aim.
The sentences would read as:
I. Politicians have promised to achieve the goal of eradicating extreme poverty many times but have failed because they cannot agree about what exactly counts as poverty and how exactly to measure it.
II. Reserve Bank hoped that a cut in its benchmark rate will achieve a reduction in inflation and improve confidence in the economy.
Option A is correct.