This result is determined as follows:
Step 1: Invert GBP quote.
First, we need to invert the GBP quotes to make the currency units USD/GBP. Then, when we multiply by the MXN/USD quote we will have the correct MXN/GBP 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 / 2.10000GBP/USD = 0.47619USD/GBP
Ask: 1.00000 / 2.00000GBP/USD = 0.50000USD/GBP
Step 2: Calculate MXN/GBP bid-ask Prices.
Bid: 8.00000MXN/USD × 0.47619USD/GBP = 3.80952MXN/GBP, or 3.81MXN/GBP.
Ask: 8.10000MXN/USD × 0.50000USD/GBP = 4.05000MXN/GBP, or 4.05MXN/GBP.
Thus, the MXN/GBP bid-ask is: 3.81MXN/GBP - 4.05MXN/GBP.