Given,
F = 4.55 i + 2.9 j ; m = 4 kg
The normal force will be:
N = mg - F sin(theta)
theta = tan^-1(2.9/4.55) = 32.51 deg
F = sqrt (4.55^2 + 2.9^2) = 5.39 N
N = 4 x 9.81 - 5.39 x sin32.51 = 36.34 N
Hence, N = 36.34 N
To move a box you pull on the handle as indicated in the diagram shown below...
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