This result is determined as follows:
Step 1: Invert GBP quote.
First, we need to invert the GBP quotes to make the currency units GBP:USD. Then, when we multiply by the USD:MXN quote we will have the correct GBP:MXN units. (Remember that when you take the reciprocal of a quote, the bid becomes the ask and vice versa. So, for the bid we take the given ask)
Bid: 1.00000 / 2.10000USD:GBP = 0.47619GBP:USD
Ask: 1.00000 / 2.00000USD:GBP = 0.50000GBP:USD
Step 2: Calculate GBP:MXN bid-ask Prices.
Bid: 8.00000USD:MXN × 0.47619GBP:USD = 3.80952GBP:MXN, or 3.81GBP:MXN.
Ask: 8.10000USD:MXN × 0.50000GBP:USD = 4.05000GBP:MXN, or 4.05GBP:MXN.
Thus, the GBP:MXN bid-ask is: 3.81 - 4.05.