The quotation comes from James Anderson and Eric Van Wincoop "Trade Costs" in the Journal of Economic Literature Vol. XLII (September 2004) pp. 691–75 and a preprint of the article is available
The calculation is trying to find the equivalent to an ad valorem tax by which the price of manufacture increases by the time of retail sale. Essentially it is saying transportation multiplies price by $1.21$ (a $21\%$ increase), tariff and non-tariff border related trade barriers multiply by $1.44$ (a $44\%$ increase), and retail and wholesale distribution costs multiply by $1.55$ (a $55\%$ increase) combining to multiply by $1.21\times 1.44\times 1.55=2.7$ (a $170\%$ increase).
This figure being over $100\%$ is not an issue. For example you could imagine a high tax on a packet of bottle of perfume costing $\$10$ before tax: if the tax rate was $170\%$ ad valorem this would add $\$17$ tax and make the after-tax price $\$27$.
There are plenty of caveats: domestic commerce also faces retail and wholesale distribution costs as well as some transport costs. Some goods see smaller costs, such as high-value low-weight goods seeing lower transport costs, or cross-border trade involving a short distance and a free-trade area, so this is in a sense a weighted average across goods and countries.
The article goes into considerable detail on the methods used for the calculations and possible implications for trade models.