I got part a but part b I'm having trouble with I keep getting 56.2mL.

I'm not sure what the next step is really to find part b.
A. How would you prepare 250 mL of a 0.150 M solution of CoCl2 from solid CoCl2 and distilled water?
Dissolve 4.87 grams solid CoCl2 into enough water to make 250mL of solution using a volumetric flask.

b. Using the solution prepared in part a and distilled water, how would you prepare 100 mL of a 0.0600 M solution of CoCl2?
Measure mL of the 0.150 M CoCl2 solution using a volumetric pipet into a volumetric flask and add enough water to bring the solution level up to the line.

2 answers

.150 to .06 is diluting it 150/6 times, or 25 tims. diluting something 25 times means 1 part base solution, adding 24 parts water.

you want 250ml, so one part is 10ml

take one part (10ml) of .150M, add 240ml of water, stir, and label.
I believe Mr. Pursley meant .150 to .06 is 15.0/6 = diluting 2.5 times. Just a typo.