In 3D, I set a variable, for example,cell variable C_R(c,t) with the coordinate i,j,k. How can I determine neighborhood cell C_R(c,t) with the coordinate i+1,j,k or i-1,j,k...in a thread.

You loop over the cell faces (if you are using hexahedral cells you will have 6 faces) with c_face_loop and then for every face there are F_C0 and F_C1 macros giving you the cell_t index, and THREAD_T0 and THREAD_T1 macros giving you the threads( if the face is a boundary face, THREAD_T1 and F_C1 does not exists).