Avoid parallels of fifths and octaves, [follow the] Shortest path principle and linearity.
Notice how the tenor voice in measure 4 leaps down from D4 to A3? This is where your version gets funky. That is probably the "clue" that you didn't see. The more natural solution, which the book's author gives, is to have the tenor go from D4 to C4 and make the alto move up with the soprano from the F4 to an A4.
There are many ways to learn and teach species counterpoint, so I will not attempt to dissect the guidelines present in this question. However, most would consider the student version with the tenor leap to be a stylistic error, generally placed in the broad category of "crossed voices". The issue is that the tenor sings a note that is below the bass note of the previous chord; many schools of four-part writing hold this to be a mistake. In essence,
No voice should cross over the note of any upper or lower voices. Additionally, no voice should cross over the previous note of any upper or lower voices.
Anything beyond the previous note is fair game, though, so for example the highest note of the tenor part may be above the lowest note of the alto part so long as they are separated in time.
Bonus points: the reason that this is considered a "rule" in many pedagogical environments is that crossed parts detract from the independence of the voices, which is kind of the whole point of this composition style. In fact, most contrapuntal rules were devised specifically to preserve the polyphonic texture. If one voice jumps above the other, it becomes very difficult to track the individual melodies.
Another bonus: These "rules" weren't created until well after this style had fallen out of favour (if memory serves), as they were intended to help later composers achieve this style. Bach certainly didn't care about any parallel fifths rule, but he probably cared a great deal about vocal independence, and it so happens that avoiding parallel octaves and fifths like the plague is a good way to sound like his music!