If you want to audit your enviroment to look at all your synonyms and see where they are pointing, you can use exec sys.sp_MSforeachdb to loop through databases, and even filter. It will save some coding. However, my research indicates it is probably a bad practice to rely on this undocumented function as it may have issues not forseen and fully tested. Additionally, support may drop for it in the future.

I recreated what I needed with a cursor to obtain all the synonym definitions into a temp table and display  results.

/*******************************************************
create temp table for holding synonym definitions & list of DB
*******************************************************/ 
if object_id( 'tempdb..#dblist' ) is not null
drop table #dblist;
select
*
into #dblist
from
sys.databases
where
Name not in ('master', 'tempdb', 'model', 'msdb')
and State_desc = 'ONLINE'
and Is_In_Standby = 0
if object_id( 'tempdb..#temp' ) is not null
drop table #temp;
create table #temp
(
db_namesysname
,object_idint
,namesysname
,base_object_namesysname
,server_name_hardcodedas case
when base_object_name like '%ThisDatabaseIsOkToHardCode%' then 0
when len( base_object_name ) - len( replace( base_object_name, '.', '' ) ) > 2 then 1
else 0
end
)
go
declare @DbName sysname
declare @XSQL varchar(max)
declare @CompleteSQL varchar(max)
declare db_cursor cursor fast_forward read_only local for
select
Name
from
#dblist
open db_cursor
fetch next from db_cursor into @DbName;
while @@fetch_status = 0
begin
set @XSQL =
'
insert into #temp
(
db_name
,object_id
,name
,base_object_name
)
select
db_name()
,s.object_id
,s.name
,s.base_object_name
from
sys.synonyms s
'
set @CompleteSQL = 'USE ' + @dbName + '; EXEC sp_executesql N''' + @XSQL + '''';
exec (@CompleteSQL)
fetch next from db_cursor into @DbName;
end
close db_cursor
deallocate db_cursor
go
select
*
from
#temp t