There are a few different possibilities that could be preventing the camera from autofocusing correctly. A lot depends on exactly how you are trying to tell the camera to initiate AF. All page number references below refer to the Nikon D750 User's Manual.

• If the switch on the lens is set to "M" the camera will not AF.
• If the switch on the camera body just below the lens release button is set to "M" the camera will not AF. (p.120)
• If you are fully pressing the shutter button without prefocusing first in either AF-C or AF-S mode and AF-C Priority Selection or AF-S Priority Selection, respectively, are set to Release the camera will go ahead and take the shot without first confirming focus (p.326). It may well be trying to AF, but the results may be leading you to believe it is not.
• If you are attempting to initiate AF using the AE-L/AF-L button and the custom setting f4 is set to "AE lock only" or "AE lock (hold)" AF will not be initiated. (p.361)
• If you are attempting to initiate AF using the shutter button but custom setting f4 (Assign AE-L/AF-L button) is set to "AF-ON" the shutter button can not be used to initiate AF. Use the AE-L/AF-L button instead. (p.362)
• If the Focus Selector Lock control is set to "Lock" (p.127) with no focus point selected the camera might not attempt to AF.

Note that when using AF lenses that are not AF-S lenses the AF/M switch on the camera body just below the lens release should not be set to "AF" if the lens is set to "M." Using the camera in such a situation can damage either the lens or the camera. The warning is on page 132 of the Nikon D750 User's Manual.