I'm working on multiple layers on Photoshop (CS6). Some of the layers have different layer styles like multiply. When I merge the layers together I seem to lose the transparency on some of the image, how can I sort this please?
It depends on what you're merging together. If you're going to merge the layers, I'm assuming you don't want to edit the layer later on.
Right-click the transparent layer, select Convert to Smart Object. Then right-click it again and select Rasterize Layer. Now you can merge this layer with others like usual.
If you want to merge layers, then don't use layer styles like multiply, overlay and so on.
Set the foreground color you want to protect (like that light-blue) and after that click on white space on your canvas. That should erase all pixels you don't want to see. Try different foreground colors for different results.
After that merge your layers.
Hope it helps.