60F is 15.55 C

180 F is 82.22C
delta T = 82.22-15.55 = 66.67
q = mass x specific heat x delta T
q = 100g x 4.184 x 66.67
q = 278,947 = 279 kJ.

Burning alcohol (46 g ethanol) provides 1238.43 kJ/mol. We want to know how many g ethanol to burn to provide 279 kJ.
46 g x (279/1238.43) = 10.36 g which rounds to 10.4 g.

Can someone, preferably DrBob, how to get the 46g of ethanol?

1 mol ethanol is 46 g.

CH3CH2OH = C2H5OH
C = 12; 2*12 = 24
H = 1; 6*1 = 6
O = 1; 1 x 16 = 16
24 + 16 + 6 = 46. ;-)