1. **State the problem:** Calculate the value of the expression $100000000000000000 \times 4.5 + \frac{300}{250} - 267 + \frac{4}{5} - (-2)$.\n\n2. **Recall the order of operations:** We perform multiplication and division first, then addition and subtraction from left to right.\n\n3. **Calculate multiplication:** $100000000000000000 \times 4.5 = 450000000000000000$.\n\n4. **Calculate division:** $\frac{300}{250} = 1.2$.\n\n5. **Calculate fraction:** $\frac{4}{5} = 0.8$.\n\n6. **Simplify the expression:** $450000000000000000 + 1.2 - 267 + 0.8 - (-2)$.\n\n7. **Simplify subtraction of negative:** $- (-2) = +2$. So expression becomes $450000000000000000 + 1.2 - 267 + 0.8 + 2$.\n\n8. **Perform addition and subtraction stepwise:**\n$450000000000000000 + 1.2 = 450000000000000001.2$\n$450000000000000001.2 - 267 = 449999999999999734.2$\n$449999999999999734.2 + 0.8 = 449999999999999735$\n$449999999999999735 + 2 = 449999999999999737$.\n\n**Final answer:** $449999999999999737$.