AC constant current (6 A rms) to 12 V DC
It is extremely unlikely that you have a CC AC source available.

More likely is that your LED string needs a maximum of 12 or 24 V DC for full brightness, and you need to figure this out before you can effectively ask for a solution. 

For example, most LED strings are 12 V DC. The current required varies with the number of LEDs.
These can be driven in several different ways:   


A DC power supply providing a regulated (but adjustable) supply of around 12 V. Altering the supply voltage alters the brightness.  
A Constant current LED power supply. Here you control the current through the LED string and typically don't turn the LEDs ON/OFF at a high rate. This is the type of driver used in LCD TVs for example.   
A simple regulated power supply followed by a PWM switch. Here the ratio of ON/OFF times sets the brightness of the string.