1. **State the problem:** Calculate the value of the expression $344 + 56(153 - 95)$.\n\n2. **Apply the order of operations:** According to the order of operations (PEMDAS/BODMAS), first solve the expression inside the parentheses.\n\n3. **Calculate inside the parentheses:**\n$$153 - 95 = 58$$\n\n4. **Multiply:** Now multiply $56$ by the result from step 3.\n$$56 \times 58 = 3248$$\n\n5. **Add:** Finally, add $344$ to the product from step 4.\n$$344 + 3248 = 3592$$\n\n**Final answer:** $3592$