Detect Index Coalesce
It is not completely clear what your after with your question. I assume you want to know if and importantly when an alter index .. coalesce was performed.

I think without (an in other answers already mentioned auditing setup) it is impossible to get such a date (although I would want to know if someone knows better). 

That said, the effects of an alter index coalesce can be made visible with a analyze index .. compute statistics.

create table ix_test (
  a number
);

create unique index ix_test_ix on ix_test(a);

insert into ix_test 
select
  rownum 
from
  dba_objects, dba_objects, dba_objects
where
  rownum &lt; 1e7;

commit;


Now that the table is filled, the index is analyzed and some index related values extracted:

analyze index ix_test_ix compute statistics;

select
  LEAF_BLOCKS,
  AVG_LEAF_BLOCKS_PER_KEY,
  CLUSTERING_FACTOR,
  SAMPLE_SIZE
from
  user_indexes
where 
  index_name = 'IX_TEST_IX';

LEAF_BLOCKS AVG_LEAF_BLOCKS_PER_KEY CLUSTERING_FACTOR SAMPLE_SIZE
----------- ----------------------- ----------------- -----------
          2                   19875                 1       15152


All but one row deleted and index analyzed (again):

delete from ix_test where a != 500000;
analyze index ix_test_ix compute statistics;


The query above returns the same values.

Coalescing the index:

alter index ix_test_ix coalesce;
analyze index ix_test_ix compute statistics;


The query above now returns

LEAF_BLOCKS AVG_LEAF_BLOCKS_PER_KEY CLUSTERING_FACTOR SAMPLE_SIZE
----------- ----------------------- ----------------- -----------
          1                       1                 1           1


So, there is a possibility to find out if there was a coalescing done, but it's not straight forward and probably useless, depending on your context.