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However, 168P = 32 would require you to divide both sides by the 168 to isolate your 'P' variable, giving you P = 32/168, from there, simplify your 32/168 -> 4/21.
Therefore, given that said problem, P = 4/21.
To check your solution you would plug the amount you calculated for 'P' back into the ORIGINAL equation and make sure it matches up.
168 (4/21) = 32
168/1 * 4/21 = 32
Cross multiply 168 x 4 / 21 x 1 = 32
= 672/21 = 32
Simplify 672/21 down to 32.
32 = 32
Correct solution.