Press the gear Tab at the bottom of the page

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When the tab has been pressed a window will open.
Move the desired piece to be enhanced.

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At lower levels these are all you will need to improve to level 4.

When you want to go higher than than that you will require an Amulet and Lucky (Gloom) stone to improve your odds of enhancing.

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As you can see by the picture above it says Amulet but that is in fact the Shaikan Charm.

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You can place the Amulet and stones into position by clicking on the picture in the right hand area under your weapons.
The higher you want to enhance the weapons the higher the Dragon Gem and Gloom Stone will need to be to help with the success rate.
The Better the Gloom Stone the Better your chance of enhancing.

Finally you can chose what level you can enhance your gear to by pressing the down arrow, (V) button and using the Instant Enhance after scrolling to that level.

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You will of course require enough Stones and Amulets before you use this feature.

Finally I hope you enjoy the game as much as I do (Happy Gaming)