Can magma do this?

Yes. Define a poly ring, define f to be 6x^2 + 8x+2, then evaluate f(f(f(f(f(x)))))

 

What, you want to solve a problem by pouring molten rock on it? How do you turn in the solution to your teacher?

 

If you don't know how to use magma, then why do you want to use magma? Start with the magma documentation if you want magma help.

The answer can be worked out by hand easily (if laboriously).

If you want to learn magma this seems like a strange way to go about it.

 

This is Mathematica code (and output). Hopefully you can convert it to the hot stuff.

Code (Text):

In[10]:= Expand[Nest[6*#1^2 + 8*#1 + 2 & , x, 5]]

Out[10]= 3074457345618258602 +
   147573952589676412928*x +
   3431094397709976600576*x^2 +
   51466415965649649008640*x^3 +
   559697273626439932968960*x^4 +
   4701457098462095436939264*x^5 +
   31734835414619144199340032*x^6 +
   176808368738592374824894464*x^7 +
   828789228462151756991692800*x^8 +
   3315156913848607027966771200*x^9 +
   11437291352777694246485360640*x^10 +
   34311874058333082739456081920*x^11 +
   90068669403124342191072215040*x^12 +
   207850775545671558902474342400*x^13 +
   423124793075117102051465625600*x^14 +
   761624627535210783692638126080*x^15 +
   1213839250134242186510142013440*x^16 +
   1713655411954224263308435783680*x^17 +
   2142069264942780329135544729600*x^18 +
   2367550240199915100623496806400*x^19 +
   2308361484194917223107909386240*x^20 +
   1978595557881357619806779473920*x^21 +
   1483946668411018214855084605440*x^22 +
   967791305485446661862011699200*x^23 +
   544382609335563747297381580800*x^24 +
   261303652481070598702743158784*x^25 +
   105526475040432357168415506432*x^26 +
   35175491680144119056138502144*x^27 +
   9422006700038603318608527360*x^28 +
   1949380696559711031436247040*x^29 +
   292407104483956654715437056*x^30 +
   28297461724253869811171328*x^31 +
   1326443518324400147398656*x^32