lambda calculus reduction: (((lambda f (lambda x (f x))) (lambda y (* y y))) 12)
Lambda expressions are evaluated by reducing the leftmost redex first.  A redex is something of the form $(\lambda a.b)c$ .  Your expression is $(\lambda f.\lambda x.fx)(\lambda y . *yy)~12$.  So your first redex is

$$(\lambda f.\lambda x.fx)(\lambda y . *yy)$$

So you substitute $(\lambda y . *yy)$ for $y$ in $\lambda x.fx$ to get $$\lambda x.(\lambda y . *yy)x~ 12$$

Then your next redex is the entire expression, ($(\lambda y . *yy)x$ is also a redex but it isn't the leftmost one) substituting $12$ in for $x$.  So you get $$(\lambda y . *yy)~12$$

Then your last redex is the entire expression again so you get

$$*~12~12$$