How to calculate transmission capacity?
The question as stated doesn't make sense. In particular, "sixteen frequencies per bit time" doesn't mean anything. So, I'll try to guess at what the question actually is, and try to point you in the right direction.

Let's break the question in two parts. First, we're told that the carrier can have eight different amplitudes. This means we can encode three bits in the carrier amplitude. If we label amplitudes $L_0,\ldots,L_7$, we can encode the bit sequence $000$ as amplitude $L_0$, $001$ as amplitude $L_1$, etc. This means that this carrier can transmit bits 3 times faster than a carrier with only two allowed amplitudes.

The second part of the question seems to indicate that you actually have sixteen carriers, all operating simultaneously. (and that they don't interfere with each other). Each carrier can have eight different amplitudes.

If you take $R$ as the baseline rate obtained by a single carrier with two amplitudes, you should now be able to calculate the rate of 16 carriers with 8 amplitudes each, as a multiple of $R$.



Edit: I think there is a second possible interpretation of the question: this could be some sort of combination ASK-FSK, where there are 16 possible frequencies (FSK) and each could have 8 possible amplitudes (ASK). Each frequency would carry 4 bits and each amplitude a further 3 bits, for a total of seven bits per symbol time.