If one variable is directly proportional to another (say z is directly proportional to x), then
z = kx
where k is a constant (the constant of proportionality.)
On the other, when z is inversely proportional to x, we can write
z = C/x
where C is a constant. In your problem, z depends on both x and y, and we are told that z is directly proportional to x and inversely proportional to y. We can express this relationship as
z = Kx/y
for some constant K.
Now to solve your problem, we must first find the constant K. We use that fact that if x = 14 and y = 10, then z = 26.6
26.6 = (K·14)/10
26.6 = 1.4K
K = 26.6/1.4
K = 19
Now we have z = 19x/y, and we can find the value of z when x = 24 and y = 15.
z = (19·24)/15
z = 30.4
Hope that helps! Let me know if you need any more help.