Note that you need to use == for equality and that it's usually a good idea to use lower case variables as Mathematica variables are upper case. However, it appears that your problem cannot be solved symbolically.
In[2]:= DSolve[{f''[t] == (f[t])^2 + h[t] f'[t] - (g[t])^2,
g''[t] == 2 f[t] g[t] + h[t] g'[t],
h'[t] == -2 f[t],
p'[t] == 2 f[t] h[t] - 2 f'[t]}, {f[t], h[t], g[t], p[t]}, t]
Out[2]= DSolve[{(f^\[Prime]\[Prime])[t] ==
f[t]^2 - g[t]^2 + h[t] Derivative[1][f][t], (g^\[Prime]\[Prime])[
t] == 2 f[t] g[t] + h[t] Derivative[1][g][t],
Derivative[1][h][t] == -2 f[t],
Derivative[1][p][t] == 2 f[t] h[t] - 2 Derivative[1][f][t]}, {f[t],
h[t], g[t], p[t]}, t]
