1. Lie on your stomach with your arms by your sides.

2. Lie on your stomach with your hands by your sides.

3. Lie on youir wtomach with your hands on your both sides.

4. Lie on your stomach with your hands on/by your side(s)
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Which one is right? Do we have to use 'by' or 'on'? Do we have to use 'side' or 'sides'?

5. Lie on your face on the floor with your hands by your sides. (What about this one?)

One has (usually) two hands and two sides. "sides" is appropriate. In #3, "both" is redundant. We only have two sides.

"by" and "on" are synonymous in this context.

#5 is fine.

Actually, "by" and "on" are not exactly synonymous. "by" doesn't mean touching your sides; "on" does.

All four options can be correct, depending on the intended meaning and the usage of prepositions and plurals. Let's break down each option:

1. Lie on your stomach with your arms by your sides.
This option suggests that you should lie on your stomach, while keeping your arms next to you, beside your body. It uses the preposition "by" to indicate the position of your arms in relation to your sides.

2. Lie on your stomach with your hands by your sides.
Similar to option 1, this choice suggests lying on your stomach, but specifies that only your hands should be beside your body. The use of "hands" instead of "arms" is more specific here.

3. Lie on your stomach with your hands on your both sides.
This option suggests lying on your stomach and placing your hands on both sides of your body. It uses the preposition "on" to indicate the position of your hands touching both sides, rather than being next to your sides.

4. Lie on your stomach with your hands on/by your side(s).
This option allows for some flexibility in the placement of your hands. It suggests that you can place your hands either directly on your sides or beside your sides. By using "side(s)" in parentheses, it indicates that you have the option to choose one side or both sides.

Ultimately, the choice between using "by" or "on" depends on whether the intended position is next to your sides or directly touching your sides. Similarly, the use of "side" or "sides" depends on whether you want to specify a single side or both sides. Consider the context and the desired placement to determine which option is the most appropriate.