You have six 1.5 kω resistors.

part a

how can you connect them to produce a total equivalent resistance of 1.0 kω ?

Have three pairs of 1.5kΩ connected in series and then connect all three in parallel.

Explanation:

This problem is kind of hard to explain and is based off my experience and intuition. I'll show how I got the answer and then explain afterwards.

If you have three pairs of 1.5kΩ in series, you get 3 3.0kΩ resistor equivalent (resistors in series). Putting them in parallel, you use get a resistance of 1 kΩ as shown below:

How I got here takes some math sense. Since 1.5kΩ is greater than 1.0kΩ, you know there is a parallel combination. Next I considered what are the possible combinations. Since two 1.5kΩ resistors yielded 3.0kΩ, and you have 3 pairs of 3.0kΩ resistor, the sum of parallel would be 1.0kΩ