step 1
Find out the slope of line 1
we have
2x+8y=-24
isolate the variable y
8y=-2x-24
y=-(2/8)x-24/8
y=-(1/4)x-3 -----> equation in slope-intercept form
the slope is m=-1/4
step 2
Find out the slope of line 2
48y=-12x-14
isolate the variable y
y=-(12/48)x-14/48
y=-(1/4)x-7/24
the slope is m=-1/4
step 3
Compare their slopes
m1=-1/4
m2=-1/4
the slopes are equal
that means
the lines are parallel
the answer is option A