To solve the system of equations, we can use the method of substitution or elimination.

a) Using the method of substitution:
From the first equation, we can solve for x in terms of y:
4x + 2y = -8
4x = -2y - 8
x = (-2y - 8)/4
x = -0.5y - 2

Substituting this expression for x into the second equation:
4x - 10y = 4
4(-0.5y - 2) - 10y = 4
-2y - 8 - 10y = 4
-12y - 8 = 4
-12y = 12
y = -1

Substituting the value of y back into the first equation:
4x + 2(-1) = -8
4x - 2 = -8
4x = -6
x = -1.5

Therefore, the solution to the system of equations is x = -1.5 and y = -1.

b) Using the method of elimination:
We can multiply the first equation by 4 and the second equation by 2 to eliminate the x term:
2(2x + y) = 2(-1)
3(3x + 4y) = 3(6)

This simplifies to:
4x + 2y = -2
6x + 8y = 18

Now we can multiply the first equation by -3 and add it to the second equation to eliminate the x term:
-3(4x + 2y) = -3(-2)
6x + 8y = 18

This simplifies to:
-12x - 6y = 6
6x + 8y = 18

Adding the two equations together:
-12x - 6y + 6x + 8y = 6 + 18
-6x + 2y = 24
-3x + y = 12

Now we can solve for y in terms of x:
y = 12 + 3x

Substituting this expression for y back into the first equation:
2x + (12 + 3x) = -1
2x + 12 + 3x = -1
5x + 12 = -1
5x = -13
x = -2.6

Substituting the value of x back into the expression for y:
y = 12 + 3(-2.6)
y = 12 - 7.8
y = 4.2

Therefore, the solution to the system of equations is x = -2.6 and y = 4.2.