The make files for RMSDK 9 or RMSDK 10 are only supported up to Android NDK-r9. If you try to build without editing the build files to support NDK-r10 you may see the following error:
clang: error: unknown argument: '-finline-limit=10000'
You can download NDK-r9d from this Google site.
If you want to use Android NDK-r10 edit the /build/make/android-ndk.tools and DLBuildAndroidExternals.mak files.
For the Android-ndk.tools file, search for ndk-r9 and change it to ndk-r10. You should find this in two locations, about lines 62 and 187 if working with RMSDK-10_0_2014-08-25.
ifneq (,$(findstring android-ndk-r10,$(ANDROID_NDK)))
DLBuildAndroidExternals.mak has the same issue around line 73.
Note also that both point to GCC 4.6. You can change this to 4.8 if needed.
These values must match what you have set in your path (arm-linux-androideabi-4.6):