How to reduce voltage without using Transformer?
Since you need a 6V DC I would suggest to use a DC/DC converter. Rectify and smooth the 24V, and use a "buck" converter, aka "switcher" or "SMPS" (Switch-Mode Power Supply).
These require only a few parts; National has a Webench web application which helps you with the design, up to the BOM. For instance, Webench shows a design around an LM2674-ADJ with a BOM cost less than USD 2.00 (sic) and an efficiency of 85%.