ANS:B - 1 BTU/ft².hr.°F/inch = 1.488 kcal/m². hr.°C/m

Let's analyze each unit conversion:

1. 1 BTU/ft2.hr.°F/ft=1.488 kcal/m2.hr.°C/m1BTU/ft2.hr.°F/ft=1.488kcal/m2.hr.°C/m - This conversion appears to be correct, as it converts between British Thermal Units per square foot per hour per degree Fahrenheit to kilocalories per square meter per hour per degree Celsius per meter.
2. 1 BTU/ft2.hr.°F/inch=1.488 kcal/m2.hr.°C/m1BTU/ft2.hr.°F/inch=1.488kcal/m2.hr.°C/m - This conversion also appears to be correct, as it converts between British Thermal Units per square foot per hour per degree Fahrenheit per inch to kilocalories per square meter per hour per degree Celsius per meter.
3. 1 kcal/m.hr.°C=0.672 BTU/ft.hr.°F=1.163 W/m.°K1kcal/m.hr.°C=0.672BTU/ft.hr.°F=1.163W/m.°K - This conversion is incorrect. The values are incorrect. The correct conversion factor for 1 kcal/m.hr.°C1kcal/m.hr.°C to British Thermal Units per foot per hour per degree Fahrenheit would be approximately 0.6720.672, but the value provided is 0.6720.672. Similarly, the conversion to watts per meter per degree Kelvin is also incorrect.
4. 1 W/cm.°C=85.985 kcal/m.hr.°C=57.779 BTU/ft.hr.°F1W/cm.°C=85.985kcal/m.hr.°C=57.779BTU/ft.hr.°F - This conversion is incorrect. The values are incorrect. The correct conversion factor for 1 W/cm.°C1W/cm.°C to kilocalories per meter per hour per degree Celsius would be approximately 85.98585.985, but the value provided is 85.98585.985. Similarly, the conversion to British Thermal Units per foot per hour per degree Fahrenheit is also incorrect.