Step 1: Set up the comparison the question is really asking for.
The question wants the slowest and most primitive of four movement types, so line all four up by what structure powers them.
Step 2: Gliding locomotion.
Some protozoans, like gregarines, glide smoothly over surfaces using an internal contractile system beneath the cell membrane, without any external moving structure. This is a fairly specialized, controlled method.
Step 3: Ciliary locomotion.
Organisms such as Paramecium are covered in many short cilia that beat in coordinated waves, driving the cell forward quickly and in a controlled direction. This needs a lot of coordinated structure.
Step 4: Euglenoid locomotion.
Euglena uses metaboly, a flexible bending and wriggling of its whole body along with flagellar beating, again a fairly elaborate, structured way of moving.
Step 5: Amoeboid locomotion.
Amoeba has none of these dedicated structures. It simply pushes cytoplasm forward into blunt, temporary bulges called pseudopodia, and the rest of the cell flows after it. There is no permanent organelle involved, the direction is not fixed, and the whole process is slow.
Step 6: Rank them by structural complexity and speed.
Because it depends on nothing more than shifting cytoplasm, with no cilia, flagella, or contractile fibers, amoeboid movement is both the slowest and the evolutionarily earliest of the four, the others all evolved dedicated structures for faster, more directed motion.
Final Answer:
Amoeboid locomotion is the most primitive and slowest type, option (2).