Implement an 8 input AND gate with least delay
I won't give a complete answer, since I assume this is homework, plus I don't really know the answer :). It's been a while since I've studied this, so I don't remember all of the terminology either.

The load of 4000 in logical-effort units is pretty large. You could make an 8-input AND gate using a tree of 2-input NAND gates with a depth of 3 followed by an inverter. That would be 4 stages, which you have already determined is not optimal to drive such a high load.

My suggestion is to do the NAND operation at the beginning and follow it with enough inverters to get to the desired strength, since inverters are simpler and have less of a scaling factor for logical effort 

What I'm not sure about is whether it is more efficient to implement the NAND as a tree of 2-input NAND gates or just as an 8-input gate directly. In real life it's hard to implement an 8-input gate directly because you don't usually have enough supply voltage, but maybe that's not considered for this academic problem. Wikipedia states that the logical effort for an 8-input NAND gate is \$\dfrac{n+2}{3} = \dfrac{10}{3}\$, and I suppose that's a single stage.