O O O
 O O O
O O O

nearby pennies touching. By the fewest number of legal moves, transform the pattern into the pattern

   O
  O O
 O   O
O O O O

nearby pennies touching. A legal move consists of sliding a penny, not picking up a penny, without disturbing the other pennies, to a new position touching at least two pennies.

I did find this easier than Sliding Pennies # 1, as I was able to work it out logically instead of using trial and error.

It looks long and involved but it wasn't. Really.

I've put my solution below, if anyone's interested. If you are, I hope it's easy enough to understand.

I aimed to do it by moving only 4 pennies. First I superimposed the start diagram over the finish one:
a)...O
....O..O..O
..O..O..O
O..O..O..O
From this I can see that the two pennies underlined must be moved from their original positions, and the two pennies in bold must be moved to the above positions.

So the penny in the center must be moved. But to move it I must first move 2 in the side if the triangle, in order to slide it out. That makes up my quota of 4 pennies to move (2 underlined in diagram a + 2 side ones).

The 2 side pennies are shown below, either A, B or C.
b)...O
....C..A..O
..C..O..A
O..B..B..O

To achieve 4 moves, each of the 4 penny can be moved only once, so must be moved directly to their finishing positions.

Neither of the underlined pennies in diagrams a & b can be moved first.
* The center one can obviously not be moved until both side ones are removed.

* The underlined penny nearer the top (diagrams a & b) could be moved to one of the positions shown in bold in diagram a. However if I do this only one of the two side pennies (A, B or C in diagram b) can be moved to its final position.
For example if move the underlined penny it would have to go to a final position of either A or B (shown below, diagram c). But then I must move both of the side pennies before moving the center one, and for these two pennies there is only one final position available (the other position is either occupied by the underlined penny that I moved first, or would block the center penny from sliding out).

Therefore I must move the 2 side pennies first, and their final positions must be as shown in bold at c.
c)...O
....O..O..O
..O..O..O
O..O..O..O

I can not move A because I would have to move the underlined one in diagram d first.
d)...O
....C..A..O
..C..O..A
O..B..B..O

I can move either B or C pennies first, not A.
If I move C my process is as shown below. Or I could move B, for steps see Sing4TheDay's answer.
If I move C my first step will be:
1). .O
....O..O..O
..X..O..O
O..O..O..  (X denotes place penny was moved from)
My second step will be:
2). .O
....X..O..O
..X..O..O
O..O..O..O

If I move the underlined penny third it will block the center penny, so I will move the center penny out first and my third step must be:
3). .O
....X..O..O
..O..X..O
O..O..O..O

And finally I will fill up the gap with the underlined penny.
3). .O
....O..O..X
..O..X..O
O..O..O..O