Delete data from a specific partition in MS SQL 2012
This delete statement is invalid SQL Server 2012 syntax so it will do nothing but raise an error. 

Removing a partition and it's associated boundary is done with MERGE DDL; DML statements like DELETE never remove partitions.

The most efficient way to remove all rows from a partition in SQL 2014 and earlier versions is with SWITCH (SQL 2016 allows specific partitions to be specified with a TRUNCATE). To use SWITCH, create a similarly partitioned staging table with identical schema and indexes. You can then switch data between tables as a meta-data operation and then TRUNCATE the staging table.

ALTER TABLE dbo.YourTable
    SWITCH PARTITION 1 TO dbo.YourTable_Staging PARTITION 1;
ALTER TABLE dbo.YourTable
    SWITCH PARTITION 2 TO dbo.YourTable_Staging PARTITION 2;
ALTER TABLE dbo.YourTable
    SWITCH PARTITION 3 TO dbo.YourTable_Staging PARTITION 3;
ALTER TABLE dbo.YourTable
    SWITCH PARTITION 4 TO dbo.YourTable_Staging PARTITION 4;
ALTER TABLE dbo.YourTable
    SWITCH PARTITION 5 TO dbo.YourTable_Staging PARTITION 5;
TRUNCATE TABLE dbo.YourTable_Staging;