1. **State the problem:** Calculate the value of $34 + 65 \div 6 \times 4$. 2. **Recall the order of operations:** According to the order of operations (PEMDAS/BODMAS), division and multiplication are performed before addition, and they are evaluated from left to right. 3. **Perform the division first:** $$65 \div 6 = \frac{65}{6} \approx 10.8333$$ 4. **Multiply the result by 4:** $$10.8333 \times 4 = 43.3333$$ 5. **Add 34 to the product:** $$34 + 43.3333 = 77.3333$$ 6. **Final answer:** $$77.3333$$ or exactly $$34 + \frac{65}{6} \times 4 = 34 + \frac{260}{6} = 34 + \frac{130}{3} = \frac{102}{3} + \frac{130}{3} = \frac{232}{3} \approx 77.3333$$