In starfish, pink boy color(p) is dominant to orange(p) , and thick eyebrows(t) are dominant over thin(t) ones. patrick , who is heterozygous for body color but purebred for thick eyebrows , has met patti , who is recessive for both traits. what's patti's phenotype? is it possible for the new couple to have offspring that resmeble their mother? explain?

Phenotype is the actual description of the traits based on the genotype. The genotype of Patti is pptt both recessive so both recessive traits are expressed. So her phenotype is orange-colored with thin eyebrows. 

To answer your question 2, we can use a Punnett Square:
Genotype of the parents:
PpTT and pptt

        PT       PT       pT        pT
pt   PpTt   PpTt     ppTt     ppTt
pt   PpTt   PpTt     ppTt     ppTt
pt   PpTt   PpTt     ppTt     ppTt
pt   PpTt   PpTt     ppTt     ppTt

Remember that dominant traits are always expressed. Based on the Punnett square that there is always a dominant T trait in each, which means that the offsprings of Patrick and Patti would have thick eyebrows.  The mother Patti has thin eyebrows. So the answer is no in terms of eyebrows.

When it comes to skin color, for the offsprings to be the same as their mother, the genotype of the skin color should be both pp, and there are 8 out of 16 squares, so there is a 50% chance that they will have orange skin.

If the condition is that they should have both thin eyebrows and orange skin, then the answer is it would be impossible.