The average emf induced in the secondary coil is 0.12 V when the current in the primary coil changes from 3.8 to 1.1 A in 0.14 s. What is the mutual inductance of the coils?

Answer 1

V2 = M12*dI1/dt

You want the mutual inductance M12.

The rate of change of current in loop 2 is dI1/dt = 2.7/0.14 = 19.3 amps/s

You do the numbers.

0.12 V = M12*19.3 amps/s
M12 will be in Henries

It is somewhat unusual to talk of "primary" and "secondary" coils when dealing with mutual inductance. That language is usually applied to transformers, but would be OK there, too.

Note that M12 = M21, although that is not obvious.