Inclusion Criteria:

• Histological or cytological proof of hepatocellular or biliary tract carcinomas, not amenable to curative resection or transplantation.
• Prior cancer treatment completed at least 30 days prior to being registered for protocol therapy and recovered from the acute toxicity effects of the regimen.
• Patients may have had radiofrequency ablation, cryosurgery or embolization, but must have documented progressive disease with the involved lesion, or at least one previously untreated lesion.
• Patients may have had ≤ 2 prior chemotherapy regimens.
• Prior radiation therapy allowed to < 25% of the bone marrow at least 30 days prior to being registered for protocol therapy.
• Patients with biliary obstruction must have percutaneous transhepatic drainage or endoscopic stent placement prior to starting study treatment.
• Patients with a history of malignancy are eligible provided they have been curatively treated and demonstrate no evidence for recurrence of that cancer.
• Peripheral neuropathy ≤ grade 1.
• Patients must agree to abstain from frozen or fresh grapefruit or grapefruit juice for 5 days prior to, and during treatment.
• Patients must be willing to use an effective method of contraception (hormonal or barrier method of birth control; abstinence) while on treatment and for a 12 week period thereafter.
• Females of childbearing potential must have a negative pregnancy test within 7 days prior to being registered for protocol therapy.
• Written informed consent and HIPAA authorization for release of personal health information.
• Age ≥ 18 years at time of consent.

Exclusion Criteria:

• No previous treatment with EGFR inhibitors.
• No treatment with any investigational agent within 30 days prior to being registered for protocol therapy.
• No symptomatic brain metastasis. A subject with prior brain metastasis may be considered if they have completed their treatment for brain metastasis, no longer require corticosteroids, and are asymptomatic.
• No Child-Pugh B or C liver cirrhosis.
• No active corneal erosions or history of abnormal corneal sensitivity test.
• No history of aneurysm or arteriovenous malformation.
• No hemorrhage/bleeding event > CTCAE Grade 3 within 30 days prior to begin registered for protocol therapy.
• No clinically significant infections as judged by the treating investigator.
• No condition that impairs patient's ability to swallow whole pills.
• No history of hypersensitivity to docetaxel or other drugs formulated with polysorbate 80.
• Females must not be breastfeeding.
• Patients who cannot avoid the following medications will be ineligible for the trial: midazolam, anti-mycotic agents (ketoconazole and related compounds), macrolide antibiotics (erythromycin and related compounds), nifedipine, phenobarbital, phenytoin, carbamazepine, and rifampin (induction) and anti-retrovirals (including ritonavir, saquinavir).