Study to Evaluate MK-6096 in the Treatment of Painful Diabetic Neuropathy (PDN) in Adults (MK-6096-021)

Inclusion Criteria: * Has a primary diagnosis of painful diabetic neuropathy (PDN) for at least 6 months. * Is able to understand \& use an electronic diary to complete daily questionnaires. * If female of reproductive potential, agrees to use acceptable contraception from Screening through to at least 2 weeks after last dose of study drug. * Is on a stable dose of antihyperglycemic treatment for at least 1 month, with hemoglobin A1C level of no more than 11%. * If taking an allowable around-the-clock medication for chronic pain, has been on a stable dose for at least 1 month \& agrees to stay on same dose during the study. * Agrees to not start therapy with opioids, pregabalin, gabapentin, duloxetine or any other medications used to treat neuropathic pain during the study. * Has a regular bedtime of before 1 AM (01:00). * Agrees to limit alcohol consumption to no more than 3 drinks a day, with no drinks within 3 hours before bedtime. One drink is defined as: 1) 12 ounces of beer; 2) 4 ounces of wine; or 3) 1 ounce of liquor (80 proof or 40% alcohol). * Agrees to limit caffeine consumption to no more than 5 standard 6-oz. cups of caffeinated beverages or no more than 600 mg caffeine a day, with no caffeinated beverages after 4 PM (16:00). * Agrees to maintain a relatively consistent level of activity throughout the study. Exclusion Criteria: * Is pregnant or breastfeeding, or expects to become pregnant during the study. * Expects to donate eggs or sperm during the study or within 90 days after last dose of study drug. * Has had ineffective treatment with more than 3 neuropathic pain drugs. * Anticipates need for surgery during the study. * Has another existing type of pain that is as severe as or greater than the pain under study OR is not able to distinguish the pain under study from another existing pain condition. * Has post herpetic neuralgia (PHN); small fiber predominant neuropathy (SFN); idiopathic sensory neuropathy (ISN); complex regional pain syndrome; sensory neuropathies; or pain caused by radiation/chemotherapy/amputation/human immunodeficiency virus (HIV) infection. * Has received a nerve block for pain within past 6 weeks. * Has a history of pernicious anemia, untreated hypothyroidism, or amputations other than toes. * Has a history of narcolepsy, cataplexy, circadian rhythm disorder, parasomnia, sleep-related breathing disorder, restless legs syndrome, periodic limb movement disorder, excessive daytime sleepiness, or difficulty sleeping due to a medical condition (i.e. asthma, Gastroesophageal Reflux Disease (GERD)) other than PDN. * Has any history of a neurological disorder, including: seizure disorder, stroke, transient ischemic attack, multiple sclerosis, cognitive impairment, or significant head trauma with sustained loss of consciousness. * Has a current evidence or history within past 6 months of unstable cardiovascular disorder, including: acute coronary syndrome; unstable angina; congestive heart failure; cardiogenic syncope; cardiomyopathy; or symptomatic arrhythmia. * Has a Body Mass Index (BMI) of more than 40 kg/m\^2. * Has any of the following: 1) evidence of ongoing depression or suicidality; 2) a lifetime history of bipolar disorder, a psychotic disorder, or posttraumatic stress disorder; 3) a psychiatric condition requiring treatment with a prohibited medication; or 3) other current psychiatric condition that might interfere with ability to participate in the study. * Is at imminent risk of self-harm or harm to others. * Has a history of substance abuse or dependence. Substances include alcohol, marijuana, hypnotics, other prescription drugs, \& drugs of abuse, but exclude nicotine. * Has a history of malignant cancer within past 5 years, except for adequately treated basal cell or squamous cell skin cancer or cervical cancer. * Has a history of hypersensitivity or reaction to more than 2 chemical classes of drugs, including prescription \& over-the-counter medications. * Is currently participating or has participated in an investigational study of a compound or device within past 30 days OR is not willing to refrain from participating in another study during this study. * Has a history of travel across 3 or more time zones or shift work (permanent night shift or rotating day/night shift work) within past 2 weeks, OR anticipates need to travel across 3 or more time zones during the study. * Has donated blood products or had more than 300 mL of blood drawn within past 8 weeks; has received blood products within past 30 days; OR intends to donate or receive blood products during the study. * Has previously participated in a study of MK-6096. * Is an employee and/or a family member of one of the investigators, study staff, or Merck.