How to Determine if FIR has a Linear_Phase Response w/o Matlab Given the FIR transfer function:

h(z) = $ .36 + .384z^{-1}  + .1608z^{-2} +.9712z^{-3}  + .352z^{-4} + .18z^{-5} - .2z^{-6} $

How do you determine if this transfer function has a linear - phase response.
Real-valued and causal FIR filters have a (generalized) linear phase response if and only if their coefficients satisfy either

$$h[n]=h[N-1-n]\tag{1}$$

or

$$h[n]=-h[N-1-n]\tag{2}$$

where $N$ is the filter length (number of taps).

There are four types of linear phase FIR filters, depending on the type of symmetry (even as in $(1)$ or odd as in $(2)$), and the filter length $N$ (even or odd). They have different properties, which is explained in this more detailed answer.