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Bias Stable Transisor Design Problem

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Please help with the following problem.

The DC load line and Q point of the circuit are shown next to the circuit. For the transistor, Beta=120. Find Re, R1, and R2 such that the circuit is bias stable.

Is it valid for me to do a KVL around the C-E loop using ic=4.8ma and vce=6v (ie=ic (b+1/b)) to find RE? And then get Rth=.1(1+beta)*Re?

Can I just arbitrarily choose an r1 and use rth to get r2? How do find the correct values of r1 and r2, and is my approach correct to this point?

A diagram to make things clearer is attached.

Thank you.

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I think your approach is correct. I'll go through the KVL just to make sure I am thinking the same thing you are.

18V - IC*(2k) - VCE - IE*(RE) = 0
18V - 4.8mA*(2k) - 6V - 4.8*RE*(B+1)/B = 0
18V - 4.8mA*(2k) - 6V - 4.8*RE*(1.008) = 0

This gives:

RE = 496 ohms

I would do this next:

Find VB to satisfy this bias condition. First find VE:

VE ...

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