Two bars of identical mass are at 34 °C. One is made from glass and the other from another substance. The specific heat capacity of glass is 840 J/(kg · C°). When identical amounts of heat are supplied to each, the glass bar reaches a temperature of 97 °C, while the other bar reaches 292.0 °C. What is the specific heat capacity of the other substance?

Not sure where to go with this one.

C*M*delta(t)=C*M*delta(t)??? M's cancel out.

Your formula is correct. The C ratio is the inverse of the delta T ratio, when the M's are the same.

delta T for bar 1 = 83 C
delta T for bar 2 = 258 C

Bar 2 must have 83/258 of the specific heat capacity of bar 1, which would be 270 J/kg*C