[3+ Moves] is a boost you unlock after completing Level 20 that adds 3 additional moves to your move limit at the start of a level in Hexic. In Hexic, each level has a maximum number of moves you can make. If you don't beat the level before the move count reaches zero, you lose the level and have to retry it. Because the [3+ Moves] boosts unlocks after completing Level 20, you can first use it to get the Make 'em Count achievement on Level 21, where you are given some free ones by the game. If you don't do it on Level 21, that is fine: it will unlock on any level.
1. tap on a level cube on the level screen (i.e. the screen with cubes that say 21, 22, 23, etc. indicating Level 21, Level 22, Level 23, etc.).
2. a box detailing the level will pop up:
a) to the top will be stars, highlighted to indicate how many stars you've earned on that level so far, followed by the level number (e.g. Level 24) and the score to beat to earn 3 stars (e.g. 60,000);
b) to the right will be a social leaderboard, to compare high scores with your friends
c) to the bottom, above the ''play' button, will be a list of boosts. To use the [3+ Moves] Use the boost by selecting it at the start of Level 21 (it says "+3" on it), and then pressing play. You'll know if you used it because at the start of the match it will say 'initializing boosters' and then the 'moves' count will increase by three.
Unlocking the Achievement
Once you've confirmed that you successfully activated the boost, it's crucial that you succeed since you only have a limited number of tries with this boost (3 of them for free). Luckily, this achievement seems to be less strict than the description indicates. The description suggests you need to "finish a level in the last 3 moves", but I found that it unlocked even though I finished the level with 10 moves to go (i.e. not in my "last 3 moves" and the achievement still popped).
You can see the moves you have remaining in the top left corner of the game screen, where it says "moves: 36", indicating that you have 36 moves remaining. After each move, the counter will drop by one (e.g. from 36 to 35). Moves only count when they lead to a combo. If you select three tiles and 'flick' them and there is no possible color match, they'll rotate back to their original position and it will not cost you a move. That said, always be careful about the direction you are rotating the tiles. While you can rotate the tiles in a backwards manner (i.e. so that it won't match up with similarly colored tiles on the first rotation but will on the second), sometimes this will result in an unintended match that will throw off your strategy.
Keeping track of your moves is especially important in the Windows Phone version of Hexic because, unlike the Windows 8/RT version of the game, in which, if you run out of moves you can watch a commercial to gain five more moves for free, there is no such free option to gain more moves at the end of a level (although, there is a paid boost you can buy).
Regarding Level 21
Level 21 is the first level with 'encryption tiles'--greyed out tiles that cannot be rotated or selected. The only way you can move encryption tiles is to decrypt them first, which is done by eliminating tiles adjacent to them, which will then 'unlock' the encryption tiles for use, with other tiles dropping into the slots). The goal of Level 21 is to eliminate all of the encryption tiles. Do that when using the [3+ Moves] boost and the Make 'em Count achievement will pop at the end of the level.
If You Run Out of Boosts
If you use up all of the free [+3 Moves] boosts the game gives you, there are two options. You can either 1) buy more, or 2) have a Facebook friend send you moves via the Windows 8 version of the game, which is itself an achievement in the Windows 8 version (thanks to Tardii for pointing this out). Because progress saves across the Windows Phone and Windows 8 versions of the game, if you receive gifts in the Windows 8 version (sending gifts is not possible in the Windows Phone version), they will appear on the Windows Phone version of your save too. To do this you need to connect Hexic (Win 8) to your Facebook account. Then you need a friend who also has Hexic (Win 8) and Facebook to do the same. Whenever you log into the game and connect to Facebook it will give you the option to either a) invite friends on Facebook to play, b) send a friend who already has the game extra lives, or c) send a friend who already has the game extra moves, which in this case would be the [+3 Moves] boost. Those three options randomly occur, so you and your Facebook friend can simply keep signing in and out of Facebook in Hexic (Win 8) until you get the 'send extra moves' options. If your friends sends you moves, the next time you sign into Facebook in Hexic (Win 8), you will be gifted the [+3 Moves] boost.