Finding the repeating unit of polymerisation given two constituent molecules
You are starting out with amino groups on one monomer and carboxylate groups on the other monomer. As William R. Ebenezer states in the comment, these combine via condensation (to form an amide, which is written as -NHCO- or -CONH- in condensed formulas). 
The linkages in the answer choices between repeating units are not visible until you write another repeating unit next to the ones shown. A. and B. show amide linkages between repeating units, while C. and D. show something else.
Here is the exercise rewritten to emphasize the amide bonds in the repeating units:

The compounds $\ce{H2NCH2CH2NH2}$ and $\ce{HOOCCH2COOH}$ react to form a polymer. What is the structure of the repeating unit of the polymer?
A. $\require{enclose}\ce{\enclose{horizontalstrike}{(}HNCH2CO-NHCH2CH2NH-CO\enclose{horizontalstrike}{)}}$
B. $\ce{\enclose{horizontalstrike}{(}HNCH2CH2NH-COCH2CO\enclose{horizontalstrike}{)}}$
C. $\ce{\enclose{horizontalstrike}{(}OCCH2CO-NHCH2NH-CO\enclose{horizontalstrike}{)}}$
D. $\ce{\enclose{horizontalstrike}{(}HNCH2CH2NH-COCH2NH\enclose{horizontalstrike}{)}}$

Now that we emphasized the amide linkages, you can see that the first monomer in A, the second monomer in C and the second monomer in D don't match your starting materials. We can also exclude C. and D. because repeating units are not linked via amides. The answer has to be B.