Step 1: Why this is not a simple trend.
You might expect basic strength to rise neatly as we add more ethyl groups, but in water that is not what happens. The actual order is set by a tug of war between electron pushing by the alkyl groups and how well water can hold on to the protonated amine.
Step 2: The two opposing factors.
Adding ethyl groups pushes more electron density onto nitrogen, which would help a tertiary amine the most. But once the amine grabs a proton, water steadies the positive ion through N to H hydrogen bonds, and a tertiary amine has the fewest such bonds, so it is steadied the least. These effects pull in opposite directions.
Step 3: The measured order for ethyl amines.
When both effects are combined for ethyl groups, experiment shows the secondary amine is most basic, then the tertiary, then the primary:
\[ (C_2H_5)_2NH > (C_2H_5)_3N > C_2H_5NH_2 \]
Step 4: Match the option.
This is exactly the order in option (D).
\[ \boxed{\text{Option (D)}} \]