Step 1: Recall the four OLAP operations.
Slicing picks one fixed value for a single dimension and looks at the resulting lower-dimension cross section, for example fixing Country = India.
Dicing picks a sub-cube by fixing a range or a set of values across two or more dimensions at once.
Roll-up moves up a dimension's concept hierarchy, combining detailed values into a coarser summary, for example City data combined into Country data.
Drill-down does the opposite of roll-up: it moves down a concept hierarchy, breaking a summarized value into its more detailed components.
Step 2: Identify the hierarchy involved here.
In a geography dimension, the usual hierarchy is Country at the top, then State below it, then City below that. Country and State sit on the same dimension (geography), with State being a finer level of detail than Country.
Step 3: Match the change in the question to an operation.
We start with Sales Quantity grouped by Product Type, Month and Country (a coarser, more summarized geography level). We want to move to Sales Quantity grouped by Product Type, Month and State (a more detailed geography level, since one Country contains many States).
No dimension is being removed (Slicing) and no dimension is being restricted to a sub-cube of specific values (Dicing), we are just moving to a lower, more detailed level of the same geography hierarchy.
Step 4: Why the other options are wrong.
(A) Slicing would mean fixing one dimension to a single value and dropping it, which is not what is happening, all three dimensions remain, only the level of detail of one of them changes.
(B) Dicing would mean selecting a sub-cube using multiple dimension restrictions, but here we are not restricting to specific values, we are changing the granularity.
(C) Roll-up would apply if we were going from State to Country (coarser), which is the reverse of what is asked here.
Final Answer:
Moving from Country (coarse) to State (detailed) within the same hierarchy is Drill-down.
\[ \boxed{\text{Option (D): Drill-down}} \]