The problem asks us to turn on all four colored light bulbs in a garland, with the restriction that a bulb can only be switched if its color differs from the one switched previously. The goal is to find the minimum number of operations needed to turn all bulbs on, or determine if it’s impossible.

There are five possible configurations of the bulbs:

1. AAAA: All bulbs are of the same color. This makes it impossible to turn on all bulbs, as you cannot alternate between different colors.
   Answer: -1.

2. AAAB: Three bulbs are of the same color, and one bulb is different. In this case, it's impossible to turn all bulbs on in just 4 moves because at least one bulb must be turned on, off, and on again, making the minimum number of operations 6.
   Answer: 6.

3. AABB: There are two pairs of bulbs with the same colors. In this configuration, you can alternate between the two pairs of bulbs and turn them all on in exactly 4 operations.
   Answer: 4.

4. AABC: Two bulbs share the same color, while the other two are different. Similarly, you can alternate between different-colored bulbs, and all bulbs can be turned on in 4 operations.
   Answer: 4.

5. ABCD: All four bulbs are of different colors. There are no restrictions in this case, and you can easily turn all bulbs on in 4 operations.
   Answer: 4.

summary For the AAAA case, so the answer is -1.
For the AAAB case, the answer is always 6 For the AABB, AABC, and ABCD cases, the answer is 4