A26-kg chandelier hangs from a ceiling on a vertical 4.0-m-long wire. what horizontal force would be necessary to displace its position 0.17 m to one side?

First of all you have that the force that is in cable in its vertical posibion is:
 Fy = m * g
 Fy = (26) * (9.8) = 254.8 N
 Then, the force in horizontal direction will be:
 Tan (x) = Fy / Fx
 Clearing:
 Fx = Fy / tan (x)
 Substituting values:
 Fx = (254.8) / (0.17 / 4)
 Fx = 5995.29 N
 
 The horizontal force that would be necessary to displace its position 0.17 m to one side is 5995.29 N