let

b = the number of gifts Ben received, b is integer

d = the number of gifts Dan received, d is integer

t = the number of gifts Time received, t is integer

Ben received three times as many gifts as Tim:

b = 3t

their neighbor Dan received 11 more gifts than Tim:

d = 11 + t

they received 65 gifts in total:

b + d + t = 65

by solving the system of equations:

b = 3t

d = 11 + t

b + d + t = 65

we find:

b = 32.4 gifts

d = 21.8 gifts

t = 10.8 gifts

click here to see the step by step solution of the system of equations:

since the number of gifts must be positive integer follows that it is impossible to divide the gifts in the described manner.