Memoryless :-
If the output at any time depends only on the input at that same time then the system is memoryless.
a) Given continuous-time system is y(t) = x(t-2)+x(2-t)
Therefore, the given system with MEMORYLESS as it at any time depends only on input.
b) Given continuous-time system is y(t) = cos(3t)x(t)
Therefore, the given system with MEMORY.
Causal :-
The output of a causal system at the present time depends on only present and/or past values of input, not on its future values.
a) Given continuous-time system is y(t) = x(t-2)+x(2-t)
Thus , the given system is NON-CAUSAL it depends on future values.
b) Given continuous-time system is y(t) = cos(3t)x(t)
Thus , the given system is CAUSAL as it depends on present values.
Linear :-
condition for linear.
a) Given continuous-time system is y(t) = x(t-2)+x(2-t)
Hence, 
Therefore , the given system is LINEAR.
b) Given continuous-time system is y(t) = cos(3t)x(t)
Hence,
Therefore , the given system is LINEAR.
Stable :-
If a system is bounded-input/bounded output is stable.
a) Given continuous-time system is y(t) = x(t-2)+x(2-t)
y(t), x(t) are bounded between -2 and 2.
Therefore , given system is STABLE.
b) Given continuous-time system is y(t) = cos(3t)x(t)
y(t) and x(t) are not bounded.
Therefore , the given system is UN STABLE.
Hope this helps you..............