Y cable will work if you just want 4 channel stereo.
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?? If you want to feed both signals (from pre and from HT) to the same power amp inputs, a Y-cable is a poor choice since the low output impedance of each source will shunt the other.
If, on the other hand, you simply want to connect 2 channels from the preamp to 8 channels of amp (with each pair of 4 channels getting the same signal), a bunch of Y-connectors will do as would a small distribution amp.
Not sure I understand what you are trying to accomplish. If you are trying to route each of the two stereo channels into four amplifier inputs, and you don't want to impact sound quality significantly, I suspect that the Behringer device is not what you want. I say that mainly because of its low price ($99 at B&H), combined with its many features.
Also, just to be sure you are aware, note that it has only balanced inputs and outputs.
There are many other pro-oriented distribution amplifiers, at all kinds of price levels, most of them also having balanced interfaces:
Using y-adapter cables is not necessarily out of the question. A four-way split (using either a 4-way y-adapter, if available, or a 2-way adapter feeding into two additional 2-way adapters) would be suitable under the following conditions:
1)The combined input impedance of the four amplifier channels is ten or more times greater than the preamp output impedance at the worst case frequency (probably 20Hz). For instance, if each of four amp channels has a 100K input impedance, the combined impedance would be 25K, and that would be suitable if the preamp output impedance at 20Hz were 2500 ohms or less.
If the input impedances of the amp channels are not all the same, the combined input impedance is the reciprocal of the sum of the reciprocals of their input impedances. For example, two 100K input impedances and two 50K input impedances result in 16.7K.
2)The interconnect cables are short enough and/or have low enough capacitance per unit length, and/or the preamp output impedance is low enough, so that the combined capacitances of the cables do not roll off the upper treble by interacting with the preamp's output impedance. Let me know if you'd like further specifics about how to calculate that.