Start by plugging in 0.1 for x in the equation
for f(x).  Then take what you get, and plug that 
in for x in the equation for f(x).

Keep taking what you get each time and plugging 
that in for x in the equation for f(x) over and over. 


f(x)=1.2x[1-x], x0 = 0.1

f(x0) = f(0.1)=1.2(0.1)[1-(0.1)] = 0.108 = x1 

f(x1) = f(0.108)=1.2(0.108)[1-(0.108)] = 0.1156032 = x2 

f(x2) = f(0.1156032)=1.2(0.1156032)[1-(0.1156032)] = 0.1226869202 = x3  

f(x3) = f(0.1226869202)=1.2(0.1226869202)[1-(0.1226869202)] = 0.1291618079 = x4 

f(x4) = f(0.1291618079)=1.2(0.1291618079)[1-(0.1291618079)] = 0.1349748422 = x5 

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Interesting fact FYI:

If you keep getting iterates for this, they will get closer 
and closer to 0.1666666... which gets closer and closer to the 
fraction 1/6.

You can tell this by setting f(x) = x and solving
                                 1.2x[1-x] = x
                                1.2x-1.2x² = x
                             -1.2x²+1.2x-x = 0  
                              1.2x²-1.2x+x = 0
                              12x²-12x+10x = 0
                                   12x²-2x = 0
                                     6x²-x = 0
                                   x(6x-1) = 0

                                   x=0;  6x-1 = 0 
                                           6x = 1
                                            x = 1/6 

If we were beginning with x0 = 0 we would of
course get 0, but if we started with any number x0 
between 0 and 1,  0 < x0 < 1 the iterations would always 
converge to (get closer and closer to) 1/6.  

Edwin