posterior part
horns
Lateral
Rubrospinal
i think it`s lumbar
Is located within the spinal cord and contains unmyelinated fibers.
Afferent impulses enter the spinal cord from the posterior section. They may get processed by interneurons. And, in most cases they exit the spinal cord through the efferent neurons in the anterior section. The reason that they refer to this as being opposite sides has to do with what are called the 'horns' inside the spinal cord. The afferent impulses enter the dorsal horns in the back and the efferent impulses exit in the front, the anterior horns. This may be why your reference, your teacher, or a book, says that impulses enter and leave from opposite sides of the spinal cord.
Lateral Spinothalamic
If you meant the 'brain' and spinal cord - it's the 'nervous system'
cranial which contains the brain and spinal which contains the nerves of the spinal cord.
The lateral extensions of the pia mater into the vertebrae are called denticulate ligaments. They anchor the spinal cord to the dura mater within the vertebral canal and help stabilize the spinal cord within the spinal column.
Horns
grey matter