When you write a line in the slope-intercept form, i.e. [tex] y=mx+b [/tex], the x coefficient, i.e. [tex] m [/tex], is the slope of the line.
So, in your case, the slope of the given line is -1/2.
If two lines with slopes [tex]m,m'[/tex] are perpendicular, then you have [tex] mm'=-1 [/tex]
So, in your case, we need a slope such that
[tex] -\dfrac{1}{2}m=-1 \iff \dfrac{m}{2} = 1 \iff m=2 [/tex]
Now, we know that we're looking for a line with slope 2 and passing through (-4,3). We can use the formula
[tex] y-y_0=m(x-x_0) [/tex]
where m is the slope and [tex] (x_0,y_0) [/tex] is a point belonging to the line. Plugging the values, we have
[tex] y-3=2(x+4) \iff y = 2x+8+3 \iff y=2x+11 [/tex]
