Identity means that the statement is ALWAYS true
Inconsistent means that the statement is NEVER true
Conditional that the statement is true under some condition only

1) -2/3z= -4/5
Simplifying, 2*5 = 3*z*4
z = 10/12 = 5/6
This is a conditional equation, since it is true for z = 5/6 but not all z.

2) 8(4-7)+6= -34
Expanding the LHS, 8*(-3) + 6 = -24 + 6 = -18. But RHS is given as -34 which
is not true. So this is Inconsistent

3) m-1= - -0.05
m-1 = 0.05 (I am assuming you have put 2 minus signs on the right side)
m = 1.05
This is also a conditional equation.

Use this approach to try out the rest yourself! Let me know if it is not
clear :)