To solve this system of equations, we can use the second equation to express x in terms of y and substitute it into the first equation.

From the second equation, we have:

x = -16 - 2y

Substituting this into the first equation:

(-16 - 2y)/2 = y/3 = z/4

Simplifying the equation:

-8 - y = y/3 = z/4

To eliminate the fractions, we can multiply all terms by the least common multiple of the denominators, which is 12:

-8(12) - 12y = 4y = 3z

Simplifying further:

-96 - 12y = 4y = 3z

Combining like terms:

-96 = 16y = 3z

Now we have a system of two equations:

16y + 3z = -96
4y = 3z

We can solve this system by substituting the second equation into the first equation:

16y + 3(4y) = -96
16y + 12y = -96
28y = -96
y = -96/28
y = -24/7

Substituting this value of y back into the second equation:

4(-24/7) = 3z
-96/7 = 3z
z = -96/21
z = -16/7

Finally, substituting the values of y and z into the expression for x:

x = -16 - 2(-24/7)
x = -16 + 48/7
x = -112/7 + 48/7
x = -64/7

Therefore, the solution to the system of equations is x = -64/7, y = -24/7, and z = -16/7.